## Algebra and Trigonometry 10th Edition

$\dfrac{x}{4}-6$
Interchange $x$ and $y$: $x=4y$ $\implies y=\dfrac{x}{4}$ Replace $y$ with $f^{-1} (x)$ or, $f^{-1} (x)=\dfrac{x}{4}$ Replace $g(x)$ with $y$. $g(x) =x+6$ Interchange $x$ and $y$: $x=y+6$ so, $y=x-6 \implies g^{-1} (x)=x-6$ Now, $g^{-1}(f^{-1} (x))=g^{-1} (\dfrac{x}{4})$ or, $=\dfrac{x}{4}-6$ or, $=(f(g(x)))^{-1}$