Question

If 𝑓⁡(𝑥)=3⁢𝑥,𝑔⁡(𝑥)=𝑥+4, and ℎ⁡(𝑥)=𝑥2−1, find [𝑔∘(𝑓∘ℎ)]⁢(−1).

Answer 1

We have (f ∘ h)(x) = f(h(x)) = 3(x^2 − 1) = 3x^2 − 3.
Then (g ∘ (f ∘ h))(x) = g(3x^2 − 3) = (3x^2 − 3) + 4 = 3x^2 + 1.
Thus (g ∘ (f ∘ h))(−1) = 3(1) + 1 = 4.