## Precalculus (10th Edition)

$f(g(x))=f(-\frac{1}{2}(x-3))=3-2(-\frac{1}{2}(x-3))=3+(x-3)=x$ $g(f(x))=g(3-2x)=-\frac{1}{2}((3-2x)-3)=-\frac{1}{2}2x=x$ There are no values to be excluded.
$f(g(x))=f(-\frac{1}{2}(x-3))=3-2(-\frac{1}{2}(x-3))=3+(x-3)=x$ $g(f(x))=g(3-2x)=-\frac{1}{2}((3-2x)-3)=-\frac{1}{2}2x=x$ There are no values to be excluded.