Question

Find the inverse function for f(x) = cubic root sqrt x+2

Answer 1

$f(x)=\sqrt[3]{x+2}\to y=\sqrt[3]{x+2}$

we replace x with y

$\sqrt[3]{y+2}=x\ \ \ \ |^3\\\\y+2=x^3\ \ \ \ |-2\\\\y=x^3-2$

Answer: $f^{-1}(x)=x^3-2$

Answer 2

we are given

$f(x)=\sqrt[3]{x+2}$

Firstly , we set f(x)=y

$y=\sqrt[3]{x+2}$

now, we can switch x and y

$x=\sqrt[3]{y+2}$

now, we can solve for y

$x^3=(\sqrt[3]{y+2})^3$

$x^3=y+2$

$y=x^3-2$

so, our inverse function is

$f^{-1}(x)=x^3-2$............Answer