Question

Suppose that

f(x) = sqrt(4 x - 7 ) g(x) = 8 x^2 - 5 .
I need: h(x) = (g o g)

h(x) = (f o f)

Answer 1

h(x) = (gog) or (fof)?

Answer 2

Yup g of g and f of f.

Answer 3

I figured they'd be the same just replace them with themselves in their x's...like an inception. Seems I was mistaken.

Answer 4

hmmm \(\bf f(x) = \sqrt{4x-7}\\
(fof)(x) = f(f(x)) = \sqrt{4(\sqrt{4x-7})-7}\) then

Answer 5

\(\bf g(x) = 8 x^2 - 5\\
(gog)(x) = g(g(x)) = 8 (8 x^2 - 5)^2 - 5\)