Given f (x) = 1/4x-3/4
Find f^-1
Answers
The inverse of a function f(x) is f⁻¹(x) = 4x + 3 after using the concept of the inverse of a function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
\(\rm f(x) = \dfrac{1}{4}x-\dfrac{3}{4}\)
To find the inverse of a function:
Interchange the f(x) and x
f(x) → x
x → f⁻¹(x)
\(\rm x = \dfrac{1}{4}f^{-1}(x)-\dfrac{3}{4}\)
Make the subject f(x);
\(\rm \dfrac{1}{4}f^-^1(x)=x+\dfrac{3}{4}\)
\(\rm f^-^1(x)=4x+3\)
Thus, the inverse of a function f(x) is f⁻¹(x) = 4x + 3 after using the concept of the inverse of a function.
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Related Questions
**PIC INCLUDED**
What is the total payment
required to pay off a promissory
note issued for $500.00 at 10%
ordinary interest and a 180-day
term?
Answers
Answer:
the total payment need to pay is $525
Step-by-step explanation:
Given that
The amount at promissory note issued is $500
The rate of interest is 10%
And, the time period is 180 days
So, the total payment included is
= $500 + ($500 × 10% × 180 days ÷ 360 days)
= $500 + $25
= $525
hence, the total payment need to pay is $525
PLSSS HELP IF YOU TURLY KNOW THISSS
Answers
Answer:24
Step-by-step explanation:
24 divided by 6 = 4
x = 4 x 6
x = 24
Kiran is spending $12 on games and rides at another carnival, where a game costs $0.25 and a ride costs $1.
Answers
Answer:
10.75 is the answer I think
365 is what percent of 55?
Answers
Answer:
636.6%
Step-by-step explanation:
To find the percent, divide 365 by 55:
365/55
= 6.636
This is equivalent to 636.6%
So, 365 is 636.6% of 55
The value of -16 is not-4 because
O A. 16² = -4
B. (-16)2.-4
C. 42
-16
D. (-4)2 = -16
SUBMI
Answers
A population's standard deviation is 15. We want to estimate the population mean with a margin of error of 4, with a 98% level of confidence. How large a sample is required? (
Answers
A sample size of 76 would be required to estimate the population mean with a margin of error of 4 and a 98% level of confidence.
How to find the sample sizeTo determine the sample size required to estimate the population mean with a specific margin of error and level of confidence, we can use the formula:
n = (Z * σ / E)²
where
n = required sample size
Z = Z-score corresponding to the desired level of confidence
σ = standard deviation of the population
E = desired margin of error
here, we have that
the standard deviation (σ) is given as 15,
the margin of error (E) is 4 and
the level of confidence is 98% and For a 98% confidence level, the Z-score is approximately 2.33.
Plugging the values into the formula:
n = (2.33 * 15 / 4)²
n = (8.7375)²
n ≈ 76.34
n = 76
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What is 4 tens, 2 ones, 7 tenths written in standard form? PLEASE DONT LIE
Answers
Answer:
(a)Seven-tenth=
7divde by 10 =0.7
(b) 4 tenth
4 divide by 10=.4
(c) 2 ones
2 multiply by1 =2
Hope it helps you.Evaluate the algebraic expression x^2 - 20 for x = 7 and for x = 9
Answers
Answer:
29
61
Step-by-step explanation:
x^2 - 20
x = 7 and 9
Evaluate
___________
We know the values of x, let's substitute them with the x in the problem :
(7)^2 - 20
49 - 20
29
(9)^2 - 20
81 - 20
61
What is the measure of the base of the rectangle if the area
of the triangle is 32 ft2 ?
Answers
Answer:
it would be a
Step-by-step explanation:
8x4=32
The base of the given triangle is calculated as: 16 ft
How to find the area of a triangle?The formula that is used to calculate the area of a triangle is expressed as:
Area of triangle= ½ × base × height
We are given that:
Area = 32 ft²
Height = 4 ft
Thus:
32 = ½ × base × 4
32 = 2 * base
base = 32/2
base = 16 ft
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Solve for x
-18 = 9 - 3x
Answers
Answer:
3x=9+18
=27
x =27÷3
x=9
the answer of x is 9
Rewrite the equation so that the x term is on the left:
9 - 3x = -18
Move the number to the right and change the sign:
-3x = -18 - 9
-3x = -27
Change the sign of both terms:
3x = 27
Move the 3 to the right and change the sign:
x = 27 ÷ 3
x = 9 is your answer.
help me fast for extra points
Answers
Answer:
EKH and FKG
Step-by-step explanation:
vertical angles are angles that are directly vertical from each other.
Answer:
C
Step-by-step explanation:
EKH AND FKG THEY ARE VERTICLE (SAME ANGLES)
a quality control expert at life batteries wants to test their new batteries. the design engineer claims they have a variance of 8100 with a mean life of 1192 minutes. if the claim is true, in a sample of 72 batteries, what is the probability that the mean battery life would be greater than 1173.8 minutes? round your answer to four decimal places.
Answers
The probability that the mean battery life would be greater than 1173.8 minutes is 0.9588
We can solve this problem using the central limit theorem, which tells us that the distribution of sample means from a population with a known variance becomes approximately normal as the sample size increases.
The standard error of the mean can be calculated as
SE = σ / sqrt(n)
where σ is the population standard deviation, n is the sample size
Here, we are given that the population variance is 8100, so the population standard deviation is the square root of 8100, which is 90.
SE = 90 / sqrt(72) = 10.6066
Next, we need to standardize the sample mean using the z-score formula
z = (X - μ) / SE
where X is the sample mean, μ is the population mean.
Here, the population mean is given as 1192 minutes and the sample mean we are interested in is 1173.8 minutes.
z = (1173.8 - 1192) / 10.6066 = -1.7356
We want to find the probability that the sample mean is greater than 1173.8 minutes. Since we have a negative z-score, we need to find the area to the right of this value on a standard normal distribution. We can use a z-table or a calculator to find this probability.
Using a standard normal distribution table, we find that the area to the right of z = -1.7356 is 0.9588.
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The mean of all possible sample means is equal to the
Select one:
a. population mean
b. population variance
c.
d. sample variance
Answers
a. population mean
The mean of all possible sample means is equal to the population mean.
This is known as the sampling distribution of the sample mean. When we take multiple random samples from a population and calculate the mean of each sample, the average of these sample means will converge to the population mean.
This is a fundamental result of statistics known as the Central Limit Theorem. As the sample size increases, the variability of the sample means decreases and they become centered around the population mean.
Therefore, the mean of all possible sample means provides an unbiased estimate of the population mean.
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Find the value of x .
Answers
Check the picture below.
\((8+16)(8)=(12+x)(12)\implies 192=144+12x \\\\\\ 48=12x\implies \cfrac{48}{12}=x\implies 4=x\)
A restaurant has a special deal where you can build your own meal from certain selections in the menu. The number of selections available in each category is shown in the table. If a person selects one of each item, how many different meals can be ordered?
Answers
Answer:
84,672 different meals
Step-by-step explanation:
Since there are 12 drink choices, we can have 12 meals with a different drink choice.
For each drink choice we can have one of seven appetizers. Therefore the combination is 12 x 7 = 84 possible combinations
For each of the above combinations we have 8 possible choices for the main entry. Thus total combos so far = 84 x 8
and so on
Thus for the number of selections shown for each category, the total possible combinations for a meal
= 12 x 7 x 8 x 14 x 9
= 84, 672 combinations
A bag contains different colored candies. There are 50 candies in the bag, 28 are red, 10 are blue, 8 are green and 4 are yellow. What is the probability of choosing one candy and getting a yellow or green? Fractions should always be in lowest terms.
Answers
Answer:
6/25
Step-by-step explanation:
you add the total number of green and yellow together to equal 12. you then divide this by the total 50 and then simplify!
hope this helps
The circumference () C of a circle is 18 18 centimeters. Which formula can you use to find the radius () r if you know that =2π C = 2 π r ? CLEAR CHECK =2π r = C 2 π =2π r = 2 C π =π2 r = π C 2 =2π
Answers
The formula to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).
The formula presented derived from the formula for the circumference of a circle, which is C = 2πr. By rearranging the equation and isolating the radius (r) on one side, we get r = C/(2π).
So, if the circumference (C) of a circle is 18 centimeters, you can use the formula r = C/(2π) to find the radius (r). Plugging in the given value for the circumference (C), we get:
r = 18/(2π)
Simplifying the equation gives:
r = 9/π
Therefore, the radius (r) of the circle is 9/π centimeters.
In conclusion, the formula you can use to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).
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Which expressions are equivalent to -
4 (16-8 +12x)?
Select all that apply.
A. 2x
B. 4 + 2 - 3x
C. - 4+2 - 3x
D. - 3x - 2
DE 3x + 2
OF 3x - 2
Answers
Step-by-step explanation:
I hope this helps..........
plssss i need helpp ASAP
Answers
Answer:
A.
1) 60
2) 27
B)
1.cm³
2.cm³
3.m³
Step-by-step explanation:
A)
5x3x4 =60cm³
3x3x3=27cm³
B)
1.cm³
2.cm³
3.m³
How heavy is 150 pounds? How much does 150 pounds weigh in kilograms? 150 lb to kg conversion.
Answers
The conversion of 150 pounds weight in kilograms 68.039.
What is meant by weight?
The gravitational force that pulls a body toward the earth or another celestial body; it is equal to the mass multiplied by the local gravitational acceleration.Weight, which is expressed in newtons, is a unit of measurement for the gravitational force acting on an object. The weight of a bird with a mass of 15 g changes with the strength of the gravitational force acting on it, and would differ significantly if it were measured, for instance, on the Moon rather than on Earth.On Earth compared to the Moon, an object would weigh differently as a result of gravity. The following is an explanation of the weight formula: Weight is calculated as mass multiplied by gravity. W = mg is the formula for this.To learn more about weight refer to
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Please help me solve this question about transformation of graphs
Answers
Answer:
You can use modern calculaters for this.
What is the value of the expression 3² .(2³+4)/2²
Answers
Answer:
27
Step-by-step explanation:
3^2(2^3+4)/2^2
3^2(8+4)/2^2
3^2(12)/2^2
9(12)/4
108/4
27
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
NO SOLUTION, cannot be graphedStep-by-step explanation:
brainliest pleaseAnswer: no solution
because that solution cant be graphed
Step-by-step explanation:
Eight of the 50 digital video recorders (dvrs) in an inventory are known to be defective. what is the probability that a randomly selected item is defective?
Answers
The probability of selecting a defective bulb is 0.16.
Given: 8 Bulbs are defective out of 50 bulbs. To find the probability that a randomly selected item is defective.
What is probability?
Probability shows the possibility of how likely an event is happening to occur out of all the possibilities.
Let’s solve the problem:
Total number of video recorders: 50
The sample space n(S) = 50
Number of defective bulbs: 8
Let E be the event of selecting a defective bulb.
Then n(E) = 8
Therefore, the probability of selecting a defective bulb: Number of defective bulbs / Total number of bulbs
=> n(E) / n(S)
=> 8 / 50
=> 0.16
Hence the probability of selecting a defective bulb is 0.16.
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40000 people visited the Emirates Park Zoo in Abu Dhabi last Year. Ratio of number of visitors of children to women to men is 4: 7: 9. Find the number of children, women and men who visited the zoo.
Answers
Answer:
40000 total visitors
Step-by-step explanation:
Let p represent a multiplier. Then the total number of visitors to the park is
4p + 7p + 9p = 40000.
This simplifies to 20p = 40000, so that p = 2000.
Then the number of children who visited is 4p = 8000; the number of women is 7p = 14000, and the number of men is 9p = 18000.
Summing up these results gives us the total number of chidren, women and men who visited the zoo last year: 8000 + 14000 + 18000, or 40000.
in how many ways can 2 red lights, 4 yellow lights, 5 blue lights, 1 green light and 2 pink lights be arranged on a string of lights?
Answers
Therefore, the total number of ways the lights can be arranged on the string is: 14! / (2! * 4! * 5! * 2!).
To find the number of ways the lights can be arranged on a string, we need to calculate the total number of permutations.
The total number of lights is 2 red lights + 4 yellow lights + 5 blue lights + 1 green light + 2 pink lights = 14 lights.
Since all the lights are distinct, we can arrange them in 14! (factorial) ways. However, since there are repetitions of certain colors, we need to account for that.
The red lights are identical, so we divide by 2! (the number of permutations of the red lights among themselves).
The yellow lights are identical, so we divide by 4! (the number of permutations of the yellow lights among themselves).
The blue lights are identical, so we divide by 5! (the number of permutations of the blue lights among themselves).
The pink lights are identical, so we divide by 2! (the number of permutations of the pink lights among themselves).
Therefore, the total number of ways the lights can be arranged on the string is:
14! / (2! * 4! * 5! * 2!)
You can calculate this expression to find the specific number of arrangements.
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7x+28 - Left Side = -6x-24 - Right side
Check left and right side of answer
Answers
Answer:
L.S = R.S ( see below)
Step-by-step explanation:
\(7x + 28 = -6x-24\\13x = -52\\x = -4\)
L.S
\(7(-4)+28 = 0\)
R.S
\(-6(-4) - 24 = 0\)
L.S = R.S
x = -4 is correct
Answer is -4
if you have a standard deviation what information does that give you about the data?
Answers
Answer:
Step-by-step explanation:
Answer:
if you have a standard deviation what information does that give you about the data?
Step-by-step explanation:
17. Use Figure 5.5. On March 20, Paul deposited $1,000 into his savings account that pays 5.5% interest
compounded daily. How much interest will the money earn by April 20?
a. $3.77
b. $4.68
C.$4.83
d. $4.98
8. On February 24, Larissa deposited $5,000 in a savings account that pays 5.5% interest compounded daily.
What will be the amount in her account on March 17?
a. $5,015.80
b. $5,031.30
c.$5,037.33
d.$5,039.80
Answers
The interest generated in Pauls savings account is $4.68
The amount generated in Larissa's savings account is $5015.80
What is Compound Interest ?Compound interest is interest that builds up over a certain length of time on both principal and interest. The principle is also used to account for the interest that has accrued on a principal over time. Furthermore, the cumulative principal value is used to calculate interest for the subsequent time period. The new way of calculating interest now utilized in all international financial and commercial operations is known as compound interest. When we look at the compound interest values that have built over various time periods, the power of compounding is clearly apparent.
The interest that is paid on both principle and interest and is compounded on a regular basis is known as compound interest. The interest is calculated for the new principal at regular intervals when the accumulated interest and the current principal are combined. The initial principal plus the interest that has already accrued make up the new principal.
The initial principal(p) of Paul is $1000
rate(r) is 5.5%
Number of days(t) = 20th March to 20th April = 31 days = 31/365 years
So the Amount generated =\(p * (1 + \frac{r}{365})\x^{365*t}\)
⇒ A = \(1000* (1 + \frac{5.5}{100*365})\x^{31} = 1000*1.00468 = 1004.68\)
The interest generated = 1004.68 - 1000 = $4.68
Similarly for Larissa
time = 24th Feb to 17th March = 21 days = 21/365 years
So the Amount generated =\(p * (1 + \frac{r}{365})\x^{365*t}\)
⇒ A = \(5000* (1 + \frac{5.5}{100*365})\x^{21} = 5000*1.00317 = 5015.80\)
The amount generated is $5015.80
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The position of an objeet moring along the x-axis is given by x=(10.0 m/s)+−(30.0 m/s2 )+ 2 +5.0 m
Answers
The average velocity of the particle over the interval from t=1.0 s to t=3.0 s is -20.0 m/s.
To find the average velocity, we need to calculate the displacement of the particle during the given time interval and divide it by the duration of the interval. The displacement can be determined by subtracting the initial position from the final position.
At t=1.0 s, the position of the object is given by x = (10.0 m/s) + (-30.0 m/s^2)(1.0 s)^2 + 5.0 m = -15.0 m.
At t=3.0 s, the position of the object is given by x = (10.0 m/s) + (-30.0 m/s^2)(3.0 s)^2 + 5.0 m = -245.0 m.
The displacement during the interval is -245.0 m - (-15.0 m) = -230.0 m.
The duration of the interval is 3.0 s - 1.0 s = 2.0 s
Therefore, the average velocity is given by the displacement divided by the duration: (-230.0 m) / (2.0 s) = -115.0 m/s.
Hence, the average velocity of the particle over the interval t=1.0 s to t=3.0 s is -115.0 meters/second.
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