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3 years ago

How do you find the inverse f-1(x) given f(x)=x^3+7?

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

4 0

Answer:

$f^{-1}(x)=\sqrt[3]{x-7}$

Step-by-step explanation:

First let me list the steps to find the inverse of a function.

1) Replace f(x) with y

2) Swap the locations of x's and y's

3) Solve for y

4) Replace y with $f^{-1}(x)$

Now lets do this with this function

$f(x)=x^3+7\\\\y=x^3+7\\\\x=y^3+7\\\\y^3=x-7\\\\y=\sqrt[3]{x-7}\\\\f^{-1}(x)=\sqrt[3]{x-7}$

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Answer:

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Step-by-step explanation:

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".

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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

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Solution to the problem

Part a

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got:

$n=(\frac{1.960(16)}{5})^2 =39.33 \approx 40$

So the answer for this case would be n=40 rounded up to the nearest integer

Part b

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