Answer
a) $x+5$
b) $x+5$
c) $x-6$
Work Step by Step
We are given the functions:
$f(x)=x+8$
$g(x)=x-3$
a) Find $f\circ g$:
$(f\circ g)(x)=f(g(x))=f(x-3)=(x-3)+8=x+5$
b) Find $g\circ f$:
$(g\circ f)(x)=g(f(x))=g(x+8)=(x+8)-3=x+5$
c) Find $g\circ g$:
$(g\circ g)(x)=g(g(x))=g(x-3)=(x-3)-3=x-6$
