Question

If f(x) = 5(x + 3)^3 – 2, then what does f^-1(x) equal?

Answer 1

`\begin{gathered} f(x)=5(x+3)^3-2 \\ \text{let f(x) = y} \\ y=5(x+3)^3-2 \\ x=5(y+3)^3-2 \\ or \\ 5(y+3)^3-2=x \\ 5(y+3)^3=x+2 \\ (y+3)^3=(x+2)/(5) \\ y+3=\sqrt[3]{(x+2)/(5)} \\ y=\sqrt[3]{(x+2)/(5)}-3 \\ f^(-1)(x)=\sqrt[3]{(x+2)/(5)}-3 \end{gathered}`