Question

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

Answer 1

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

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