the question below

Question

Consider the following functions.

f(x) = 1 square of x

g(x) = x2 − 8x

,

Find (f ∘ g)(x).

 

Find the domain of (f ∘ g)(x).

 (Enter your answer using interval notation.)

 

Find (g ∘ f)(x).

 

Find the domain of (g ∘ f)(x).

 (Enter your answer using interval notation.)

 

Find (f ∘ f)(x).

 

Find the domain of (f ∘ f)(x).

 (Enter your answer using interval notation.)

 

Find (g ∘ g)(x).

 

Find the domain of (g ∘ g)(x).

 (Enter your answer using interval notation.)

 

Answer 1

I am assuming that

f(x) = 1 square of x means f(x) = x²

Find (f ∘ g)(x).

Tuck g(x) into f(x)

(f o g)(x) = (x² – 8x)² = (x² - 8x)(x² - 8x)= x⁴ -16x³ + 64x²

Find the domain of (f ∘ g)(x).

(Enter your answer using interval notation.)

(-∞, ∞)

Find (g ∘ f)(x).

(g o f)(x) = (x²)² – 8(x²) = x⁴ - 8x²

Find the domain of (g ∘ f)(x).

(Enter your answer using interval notation.)

(-∞, ∞)

Find (f ∘ f)(x).

( f o f)(x) = (x²)² = x⁴

Find the domain of (f ∘ f)(x).

(Enter your answer using interval notation.)

(-∞, ∞)