Given f(x) = x + 3 and g(x) = x2 – 4 Find (𝑔 ∘ 𝑓)(𝑥)

Question

Given f(x) = x + 3 and g(x) = x^2 – 4 Find (𝑔 ∘ 𝑓)(𝑥)

Answer 1

(g*f)(x) = g(f(x))= g (x + 3) Since f(x) = x+3

We have g(x) = x² - 4

g(x+3) = (x+3)² - 4 = x² +6x +9 -4 = x² +6x +5 =(x+5) (x+1)

So (g*f) (x) =(x+5) (x+1)

Answer 2

g of f of x would be

=(X+3)^2-4

=(x+3)(x+3)-4

=(x^2+6x+9) - 4

=x^2+6x+5