Question

Find comp

f(x) = 2x + 3
g(x) = x2 – 3x + 1
Write g(f(x)) as an expression in terms of x.

Answer 1

g(f(x))= 4x^2 + 6x +1

Explanation:

f(x) = 2x + 3

g(x) = x2 – 3x + 1

the composition of functions can be understand as evaluating one function inside the other.

so evaluate g(f(x)) means to change the 'x' variable from g(x) by the whole expression of f(x).

g(f(x))= (2x+3)^2 - 3 (2x+3) + 1 (note that we substitute 'x' variable by the content of f(x), which is 2x+3)

If we develop the square product as well the other products, we have

g(f(x))= 4x^2+12x+9 - 6x-9 + 1

leading to

g(f(x))= 4x^2 + 6x +1