Question

for \\(f(x) = x^2 + 3\\) and \\(g(x) = x^2 - 4\\), find the following functions.
a. \\((f \circ g)(x)\\); b. \\((g \circ f)(x)\\); c. \\((f \circ g)(4)\\); d. \\((g \circ f)(4)\\)

a. \\((f \circ g)(x) = \square\\)
(simplify your answer.)

b. \\((g \circ f)(x) = \square\\)
(simplify your answer.)

c. \\((f \circ g)(4) = \square\\)

d. \\((g \circ f)(4) = \square\\)

Explanation:

Find the composition (f ∘ g)(x)

Using the Function Composition knowledge point

$$
LATEXBLOCK0
$$

Find the composition (g ∘ f)(x)

Using the Function Composition knowledge point

$$
LATEXBLOCK1
$$

Evaluate (f ∘ g)(4)

Using the Function Composition knowledge point

$$
LATEXBLOCK2
$$

Evaluate (g ∘ f)(4)

Using the Function Composition knowledge point

$$
LATEXBLOCK3
$$

Answer:

Question a

a. \((f \circ g)(x) =\) <blank>\(x^4 - 8x^2 + 19\)</blank>

Question b

b. \((g \circ f)(x) =\) <blank>\(x^4 + 6x^2 + 5\)</blank>

Question c

c. \((f \circ g)(4) =\) <blank>\(147\)</blank>

Question d

d. \((g \circ f)(4) =\) <blank>\(357\)</blank>