Question

How do you find the inverse of `f(x) = 1 - (1/x)` and is it a function?

Answer 1

Inverse of `f(x)=1-1/x` is `f(x)=1/(1-x)` or `1+x/(1-x)`

Explanation:

As `y=1-1/x`

then `1/x=1-y`

and `x=1/(1-y)=(1-y+y)/(1-y)=1+y/(1-y)`

Hence inverse of `f(x)=1-1/x` is `f(x)=1/(1-x)` or `1+x/(1-x)`