Question

How do you find `(fog)(x)` given `f(x)=2x^3-5x^2` and `g(x)=2x-1`?

Answer 1

`(2x-1)^2(4x-7)`

Explanation:

`"to evaluate" (f@g)(x)" substitute g(x) into f(x)"`

`f(color(red)(2x-1))`

`=2(color(red)(2x-1))^3-5(color(red)(2x-1))^2`

`"factor out " (2x-1)^2`

`rArr(2x-1)^2[2(2x-1)-5]`

`=(2x-1)^2(4x-7)`

`"which may be further expanded if you wish"`