(g o f)(x)=12x²+16 x-3 ,f(x)=3x²+4x-3, find g(x)

Answer 1

(g o f)(x)
is the same as f(g(x))

Observing that
12x^2 + 16x - 3
= 4(3x^2 + 4x) - 3

let g(x) = 4x

then f(g(x))
= 3(4x)^2 + 4(4x) - 3
= 12x^2 + 16x - 3 , which is what we have, so

g(x) = 4x

Answer 2

Hmmm. I thought (g o f)(x) was g(f(x)).

If that is so,
12x^2 + 16x - 3 = 4(3x^2 + 4x - 3) + 9
= 4f+9

so g(x) = 4x+9