How do you find f^-1(x) given f(x)=1/x^3?

1 Answer
Nov 23, 2016

The answer is f^(-1)(x)=1/x^(1/3)

Explanation:

Let y=1/x^3

Then, x^3=1/y

x=1/y^(1/3)

Therefore f^(-1)(x)=1/x^(1/3)

The verification is f(f^(-1)(x))=x

Let's do this

f(f^(-1)(x))=f(1/x^(1/3))=1/(1/x^(1/3))^3=1/(1/x)=x