Question

If `f(x) = x^2 - x` and `g(x) = 3x + 1` how do you find f(g(x))?

Answer 1

`f(g(x))=color(green)(3x^2+3x`

Explanation:

The problem with this type of question is often the confusion that results from two different uses of `x`

If instead we write
`color(white)("XXX")f(color(blue)(w))=color(blue)(w)^2-color(blue)(w)`
then there is less difficulty in replacing `color(blue)(w)` with `color(red)(g(x))`
`color(white)("XXX")f(color(red)(g(x)))=color(red)(g(x))^2-color(red)(g(x))`
and then replacing `color(red)(g(x))` with `color(brown)(3x+1)`
`color(white)("XXX")f(g(x)) = (color(brown)(3x+1))^2-(color(brown)(3x+1))`

`color(white)("XXXXXXX")=3x^2+6x+1-3x-1`

`color(white)("XXXXXXX")=3x^2+3x`