Question

Given `f(x)=1/(x-2)`, how do you find f(f(x))?

Answer 1

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

Explanation:

Where ever you see `x` replace it with `1/(x-2)`

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

`color(blue)("Consider just the denominator")`

Multiply the 2 by `1` but in the form of `1-(x-2)/(x-2)`

So the denominator becomes

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

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

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

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

`color(blue)("Substitute into original expression")`

`color(green)(f(f(x))= 1 -: (2x+5)/(x-2)" "=" "(x-2)/(2x+5))`