Question

Given `f(x) = (3x-1 )/( 2x+5)` and `g(x)=( 7x+3 )/( 3x-1)` how do you find f(g(x))?

Answer 1

`f(g(x))=(18x+10)/(11x+7)`

Explanation:

`f(x)=(3x-1)/(2x+5)` and `g(x)=(7x+3)/(3x-1)`

we get `f(g(x))` by putting `g(x)` in place of `x` in `f(x)`.

Hence `f(g(x))=(3*(7x+3)/(3x-1)-1)/(2*(7x+3)/(3x-1)+5)`

= `(3(7x+3)-(3x-1))/(2(7x+3)-(3x-1))`

= `(21x+9-3x+1)/(14x+6-3x+1)`

= `(18x+10)/(11x+7)`