Question 10

Explanation

Given $f(x) = \frac{2x - 5}{x - 4}$ with $x \neq 4$ and $g(x) = 3x + 8$

Determining the Composite Function

Calculate the composite function $(f \circ g)(x) = f(g(x))$

Determining the Inverse Function

Let $y = \frac{6x + 11}{3x + 4}$, then solve for $x$ in terms of $y$

Replace $y$ with $x$ to get the inverse function

The condition is $3x - 6 \neq 0 \Rightarrow x \neq 2$

Therefore, the inverse of $(f \circ g)(x)$ is $\frac{11 - 4x}{3x - 6}$ with $x \neq 2$