F(x) = 16 + \sqrt[3]{x} \\ f {}^( - 1) (x) =Inverse function

Question

`f(x) = 16 + \sqrt[3]{x} \\ f {}^( - 1) (x) =`Inverse function

Answer 1

`f^(-1)(x)=(x-16)^3`

Step-by-step explanation:

to find the inverse function, we have to solve for x.

First we subtract 16 from both sides to get

`f(x)-16=\sqrt[3]{x}`

Then raising both sides to the power of 3 gives

`(f(x)-16)^3=(\sqrt[3]{x})^3`
`x=(f(x)-16)^3`

The above we can write as

`f^(-1)(^{}x)=(x-16)^3`

because we have solved for x ( thus it has become an inverse function) which is now a function of what was previously f(x).