Answer: D
Step-by-step explanation:
f(x) = 2x g(x) = x² - 1
f(g(x)) = 2(x² - 1)
= 2x² - 2
g(f(x)) = (2x)² - 1
= 4x² - 1
Using composite function concepts, it is found that the correct statement is:
D. [tex](g \circ f)(x) = 4x^2 - 1[/tex]
The composite function definition is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
[tex](g \circ f)(x) = g(f(x))[/tex]
In this problem:
[tex]f(x) = 2x[/tex]
[tex]g(x) = x^2 - 1[/tex]
Then
[tex](f \circ g)(x) = f(x^2 - 1) = 2(x^2 - 1) = 2x^2 - 2[/tex]
[tex](g \circ f)(x) = g(2x) = (2x)^2 - 1 = 4x^2 - 1[/tex]
Then, the correct statement is:
D. [tex](g \circ f)(x) = 4x^2 - 1[/tex]
A similar problem is given at https://brainly.com/question/9484507
