Use the functions given by $f ( x ) = x + 4$ and $g ( x ) = 2 x - 6$ to find the composition of functions $(g\circ f)^{-1}$
A) $\frac { - ( x + 2 ) } { - 2 }$
B) $\frac { - x + 2 } { 2 }$
C) $\frac { x - 2 } { 2 }$
D) $\frac { x - 2 } { - 2 }$
E) $\frac { x + 2 } { 2 }$

Question

Quizplus · Accepted Answer

First, find the composition $g(f(x)) = 2(x+4)-6 = 2x+2$. Then, to find the inverse, swap $x$ and $y$ and solve for $y$, giving $x = 2y + 2$, which simplifies to $y = \frac{x - 2}{2}$.

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

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