# F(x) = (x+1)/x f o g (x) = x, what is g(x) ??

May 22, 2018

$g \left(x\right) = \frac{1}{x - 1}$

#### Explanation:

$f \left(x\right) = \frac{x + 1}{x}$

$f \left(g \left(x\right)\right) = x$

Our first step is to plug $g \left(x\right)$ into $f \left(x\right)$.

f(g(x))=(g(x)+1)/(g(x)

Now, we know that this equals $x$.

x=(g(x)+1)/(g(x)

In order to solve for $g \left(x\right) ,$ we must isolate it. We can start simplifying because $g \frac{x}{g} \left(x\right) = 1$.

$x = 1 + \frac{1}{g} \left(x\right)$

$x - 1 = \frac{1}{g} \left(x\right)$

$g \left(x\right) = \frac{1}{x - 1}$