## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

a) $acx+ad+b$ b) $acx+cb+d$ c) domain for both (a) and (b): all real numbers d) $ad+b=cb+d$
We have the composite functions: a) $(f\circ g) (x) =f[g(x)]=a(cx+d)+b\\=acx+ad+b$ b) $(g\circ f) (x) = g[f(x)]=c(ax+b) +d=acx+cb+d$ c) The domain of both composite functions is all real numbers (no restrictions). d) The functions $f(x)$ and $g(x)$ are known as inverse functions. So, we can equate $(f\circ g) (x)=(g\circ f) (x)$ or, $f[g(x)]=g[f(x)]$ as follows: $acx+ad+b=acx+cb+d \\ ad+b=cb+d$