Question

If `f(x) = x^2 + 3x` and `g(x) = 4x - 1`, what is `(f@g)(x)`?

Answer 1

In this example `g(x)` becomes the input for `f(x)`. After all of the substitutions are made foil `(4x-1)^2`, distribute `3(4x-1)` and then combine the like terms.

`(f@g)(x)`

`f(g(x))`

`f(4x-1)=(4x-1)^2+3(4x-1)=16x^2-8x+1+12x-3=16x^2+4x-2`

Please see the link below for a related example

If `f(x) = x^2` and `g(x) = x + 2`, what is `(f@g)(x)`?