Question

Find the inverse of:f (x) = 4x3 + 1

Answer 1

1. replace f(x) with y

`y=4x^3+1`

2. Replace every x with a y and replace every y with an x

`x=4y^3+1`

3. Solve for y:

`\begin{gathered} 4y^3=x-1 \\ y^3=(x-1)/(4) \\ y=\sqrt[3]{(x-1)/(4)} \end{gathered}`

4. Replace y with f−1(x):

`f^(-1)(x)=\sqrt[3]{(x-1)/(4)}`