Question

Need help with the composition of functions. I have attached a screenshot of the question.

Answer 1

(f∘f)(x) = x⁴ -12x² +30

(g∘g)(x) = x/9

Explanation:

a) (f∘f)(x) = f(f(x)) = f(x² -6)

... = (x² -6)² -6

... = x⁴ -12x² +36 -6

... (f∘f)(x) = x⁴ -12x² +30

b) (g∘g)(x) = g(g(x)) = g(x/3)

... = (x/3)/3

... (g∘g)(x) = x/9