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

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Answer 1 · 2016-04-14T07:48:21

Inverse of $f (x) = 1 - \frac{1}{x}$ $f(x)=1-1/x$ is $f (x) = \frac{1}{1 - x}$ $f(x)=1/(1-x)$ or $1 + \frac{x}{1 - x}$ $1+x/(1-x)$

As $y = 1 - \frac{1}{x}$ $y=1-1/x$

then $\frac{1}{x} = 1 - y$ $1/x=1-y$

and $x = \frac{1}{1 - y} = \frac{1 - y + y}{1 - y} = 1 + \frac{y}{1 - y}$ $x=1/(1-y)=(1-y+y)/(1-y)=1+y/(1-y)$

Hence inverse of $f (x) = 1 - \frac{1}{x}$ $f(x)=1-1/x$ is $f (x) = \frac{1}{1 - x}$ $f(x)=1/(1-x)$ or $1 + \frac{x}{1 - x}$ $1+x/(1-x)$

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