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