# Consider the function f(x)=1/(x-2), then how do you simplify f(f(x))?

Jul 28, 2016

$f \left(f \left(x\right)\right) = \frac{x - 2}{5 - 2 x}$

#### Explanation:

As $f \left(x\right) = \frac{1}{x - 2}$

Now to find $f \left(f \left(x\right)\right)$ we have to just substitute $f \left(x\right)$ in place of $x$. As $f \left(x\right) = \frac{1}{x - 2}$, to find $f \left(f \left(x\right)\right)$, we substitute $\frac{1}{x - 2}$ in place of $x$ on Right Hand Side, Hence

$f \left(f \left(x\right)\right) = \frac{1}{\frac{1}{x - 2} - 2}$

= 1/(1/(x-2)-(2(x-2))/(x-2)

= $\frac{1}{\frac{1 - 2 x + 4}{x - 2}}$

= $\frac{1}{\frac{5 - 2 x}{x - 2}}$

= $\frac{x - 2}{5 - 2 x}$