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

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Answer 1 · 2016-04-14T07:48:21

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

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 $1+x/(1-x)$

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