Question

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

Answer 1

`f(f(x))=(x-2)/(5-2x)`

Explanation:

As `f(x)=1/(x-2)`

Now to find `f(f(x))` we have to just substitute `f(x)` in place of `x`. As `f(x)=1/(x-2)`, to find `f(f(x))`, we substitute `1/(x-2)` in place of `x` on Right Hand Side, Hence

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

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

= `1/((1-2x+4)/(x-2))`

= `1/((5-2x)/(x-2))`

= `(x-2)/(5-2x)`