Find (f∘g)(x).

Question

f(x)=x–3
g(x)=2x2–5
Write your answer as a polynomial in simplest form.
(f∘g)(x)=

Answer 1

To find (f ∘ g)(x), we substitute g(x) into f(x). Therefore,

(f ∘ g)(x) = f(g(x)) = f(2x^2 - 5).

Now, substitute x - 3 into g.

(f ∘ g)(x) = f(2(x^2 - 3))

Next, distribute the 2.

(f ∘ g)(x) = f(2x^2 - 6)

Lastly, substitute x - 3 into f.

(f ∘ g)(x) = 2x^2 - 6 - 3

Simplifying, we get:

(f ∘ g)(x) = 2x^2 - 9