Question

Formula is given for function y=f(x). In each case, find f^-1(x), and identify the domain and range of f^-1. As a check, show that f(f^-1(x))=f^-1(f(x))=x.

f(x)=x^5

Answer 1

for f(x)=x^5, let y = x^5, now rearrange the equation so it's in the form x = ..., then swap x with y and y with x.

\[\Large y=x^5\]

Take the 5th root of both sides, then swap y with x and x with y.