How do you find f^-1(x) given f(x)=1/(x-1)^2?

1 Answer
Nov 5, 2016

THe answer is =1/sqrtx+1

Explanation:

Let y=1/(x-1)^2
So (x-1)^2=1/y
x-1=1/sqrty
x=1/sqrty+1
:. f^-1(x)=1/sqrtx+1
Verifications, we calculate
f(f^-1(x))=f(1/sqrtx+1)=1/(1/sqrtx+1-1)^2=1/(1/sqrtx)^2
=1/(1/x)=x

:. we have calculated f^-1(x)