Question

if \\(f(x) = 5x - 4\\) and \\(g(x) = x^2\\), find the following composite functions and state the domain of each.
(a) \\(f \circ g\\)
(b) \\(g \circ f\\)
(c) \\(f \circ f\\)
(d) \\(g \circ g\\)

Explanation:

Find the composite function (f ∘ g)(x) and its domain

Using the Composite Functions and Domain and Range knowledge points

$$
LATEXBLOCK0
$$

Find the composite function (g ∘ f)(x) and its domain

Using the Composite Functions and Domain and Range knowledge points

$$
LATEXBLOCK1
$$

Find the composite function (f ∘ f)(x) and its domain

Using the Composite Functions and Domain and Range knowledge points

$$
LATEXBLOCK2
$$

Find the composite function (g ∘ g)(x) and its domain

Using the Composite Functions and Domain and Range knowledge points

$$
LATEXBLOCK3
$$

Answer:

Question 1

• Composite Function: \((f \circ g)(x) = 5x^2 - 4\)
• Domain: \((-\infty, \infty)\)

Question 2

• Composite Function: \((g \circ f)(x) = (5x - 4)^2\) or \(25x^2 - 40x + 16\)
• Domain: \((-\infty, \infty)\)

Question 3

• Composite Function: \((f \circ f)(x) = 25x - 24\)
• Domain: \((-\infty, \infty)\)

Question 4

• Composite Function: \((g \circ g)(x) = x^4\)
• Domain: \((-\infty, \infty)\)