Use the functions $f ( x ) = x + 4$ and $g ( x ) = 5 x - 7$ to find $( g \circ f ) ^ { - 1 }$.
A) $( g \circ f ) ^ { - 1 } = \frac { 5 x + 11 } { 4 }$
B) $( g \circ f ) ^ { - 1 } = 5 x - 42$
C) $( g \circ f ) ^ { - 1 } = \frac { x - 13 } { 5 }$
D) $( g \circ f ) ^ { - 1 } = \frac { - 7 x - 7 } { 5 }$
E) $( g \circ f ) ^ { - 1 } = 5 x + 13$

Question

Quizplus · Accepted Answer

First, find $g(f(x))$: substitute $f(x) = x + 4$ into $g(x)$, getting $g(f(x)) = 5(x + 4) - 7 = 5x + 20 - 7 = 5x + 13$. To find the inverse, swap $x$ and $y$ and solve for $y$, giving $x = 5y + 13$, which simplifies to $y = \frac{x - 13}{5}$, matching choice C.

Use the Functions f(x)=x+4f ( x ) = x + 4f(x)=x+4

Use the Functions $f ( x ) = x + 4$