Question

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

Answer 1

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)`