Question

Given the functions:

f(x) = -|x - 3| + 4
g(x) = x² - 4x + 3

What is the value of (f ∘ g)(4)?

A) 3
B) 0
C) 7
D) -1

Answer 1

The value of (f ∘ g)(4) is 4.

Step-by-step explanation:

To find the value of (f ∘ g)(4), we need to substitute the value of 4 into the composite function f(g(x)). First, we need to find the value of g(4) by substituting 4 into the function g(x).

g(4) = 4² - 4(4) + 3 = 16 - 16 + 3 = 3

Next, we substitute the value of g(4) into the function f(x).

f(g(4)) = f(3) = -|3 - 3| + 4 = -0 + 4 = 4

Therefore, the value of (f ∘ g)(4) is 4 (option A).