Decide whether the composite functions, f ° g and g ° f, are equal to x.
-$$f ( x ) = \frac { x - 6 } { 4 } , \quad g ( x ) = 4 x + 6$$
A) Yes, yes
B) No, yes
C) No, no
D) Yes, no

Question

Quizplus · Accepted Answer

To determine if $f \circ g$ and $g \circ f$ are equal to $x$, we compute each composite function separately.1. For $f \circ g$, we substitute $g(x)$ into $f(x)$:$$f(g(x)) = f(4x + 6) = \frac{(4x + 6) - 6}{4} = \frac{4x}{4} = x$$2. For $g \circ f$, we substitute $f(x)$ into $g(x)$:$$g(f(x)) = g\left(\frac{x - 6}{4}\right) = 4\left(\frac{x - 6}{4}\right) + 6 = x - 6 + 6 = x$$Both $f \circ g$ and $g \circ f$ are equal to $x$, so the correct answer is A.

Decide Whether the Composite Functions, F ° G and G f(x)=x−64,g(x)=4x+6f ( x ) = \frac { x - 6 } { 4 } , \quad g ( x ) = 4 x + 6f(x)=4x−6​,g(x)=4x+6

Decide Whether the Composite Functions, F ° G and G $f ( x ) = \frac { x - 6 } { 4 } , \quad g ( x ) = 4 x + 6$