Find comp

f (x) = 2x + 3

g (x) = x2 - 3x + 1

Write g (f (x)) as an expression in terms of x.

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

Step-by-step 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