Use the functions given by f(x)= x + 2 and g(x)= 2x - 5 to find (f _º g)^-1. ? A) $\frac { x + 3 } { 2 }$ B) $\frac { x - 3 } { - 2 }$ C) $\frac { x - 4 } { 3 }$ D) $\frac { x - 3 } { 2 }$ E) $\frac { - x - 3 } { 2 }$

Question

Quizplus · Accepted Answer

The composition of functions $f(g(x))$ is calculated by substituting $g(x)$ into $f(x)$, resulting in $f(g(x)) = (2x - 5) + 2 = 2x - 3$. The inverse of this function, $(f \circ g)^{-1}(x)$, involves swapping $x$ and $y$ and solving for $y$, leading to $x = 2y - 3$, which simplifies to $y = \frac{x + 3}{2}$.

Use the Functions Given by F(x)= X + 2 and G(x)=