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2 years ago

2. Graph the inverse of the function, then determine if the inverse is a function.

Mathematics

1 answer:

charle [14.2K]2 years ago

5 0

The inverse of the function f(x)= x^2 is a function.

<h3>The graph of the inverse</h3>

The equation of the function is

f(x)= x^2

Rewrite as:

y = x^2

Swap x and y

x = y^2

Make y the subject

$y = \sqrt x$

Rewrite as:

$f^{-1}(x) = \sqrt x$

So, the inverse of f(x)= x^2 is $f^{-1}(x) = \sqrt x$

See attachment for the graph

<h3>Is the inverse a function?</h3>

The inverse is a function.

This is so because it passes the vertical line test

Read more about inverse functions at:

brainly.com/question/2883051

#SPJ1

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The area of Terry's room at the old house was 96 ft.2. The area of Terry's room at the new house is 108 ft.2

Finger [1]

Answer:

12.5%

Step-by-step explanation:

First we need to calculate the change in the area of Terry's room this is

108 ft2 - 96 ft2 = 12 ft2

Then we use a direct proportion in order to find the percentage

96 ft2 ----- 100%

12 ft2 ----- p?

Solvin for p we have that

$p=\frac{12\times 100}{96}$

p=12.5

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3 years ago

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What is the answer to this question?

dimulka [17.4K]

It decreased $7 in the last 2 days

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3 years ago

Multiply and Simplify<br> (x-4)(x^2 - 5x - 6)

kirill [66]

Answer:

x^3 -9x^2 +14x +24

Step-by-step explanation:

(x-4)(x^2 - 5x - 6)

Multiply the x by everything in the second term

x * (x^2 - 5x - 6)

x^3 -5x^2 -6x

Multiply the -4 by everything in the second term

-4 * (x^2 - 5x - 6)

-4x^2 +20x +24

Add everything together

I like to line them up vertically

x^3 -5x^2 -6x

-4x^2 +20x +24

-------------------------------

x^3 -9x^2 +14x +24

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3 years ago

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The population of Groverdale is

wolverine [178]

Answer: Yes alaina is correct

Step-by-step explanation: first look at the populations

553,000

535,841

Tittlehook has a 3 in the ten thousands place whilst groverdale has a 5 in the thousands place.

Hope this helps :)

6 0

3 years ago

A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at th

Valentin [98]

Answer:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=12.8$

The sample deviation calculated $s=4.324 \approx 4.3$

$12.8-4.604\frac{4.324}{\sqrt{5}}=3.896$

$12.8+ 4.604\frac{4.324}{\sqrt{5}}=21.704$

So on this case the 99% confidence interval would be given by (3.896;21.704)

Step-by-step explanation:

Data: 10,9,20,13,12

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=12.8$

The sample deviation calculated $s=4.324$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=5-1=4$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,4)".And we see that $t_{\alpha/2}=4.604$

Now we have everything in order to replace into formula (1):

$12.8-4.604\frac{4.324}{\sqrt{5}}=3.896$

$12.8+ 4.604\frac{4.324}{\sqrt{5}}=21.704$

So on this case the 99% confidence interval would be given by (3.896;21.704)

6 0

3 years ago