Question

For all values of x,

f(x) = 2x - 3
and
g(x) = x2 + 1
a) Find fg(x).
Simplify and give your answer in the form ax2 + b
b) Find gf(x).
Simplify and give your answer in the form ax2 + bx + c
I DONT NEED THE ANSWER TO A, I JUST NEED B

Answer 1

The composition g(f(x)) is:

`g(f(x))=4x^(2)-12x+10`

Explanation:

b) g(f(x)) is a function composition.

So we will have:

`g(f(x))=(f(x))^(2)+1`

`g(f(x))=(2x-3)^(2)+1`

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

`g(f(x))=4x^(2)-12x+10`

Here:

a is 4

b is -12

c is 10

I hope it helps you!