Answer
(a.) $(f\circ g)(x) =3x-15$.
(b.) $(g\circ f)(x) =3x-5$.
(c.) $(f\circ g)(2) = -9$.
Work Step by Step
The given functions are
$f(x)=3x$ and $g(x)=x-5$.
(a) $(f\circ g)(x) = f(g(x))$
Replace $x$ with $g(x)$ in the function $f(x)$.
$f(g(x))=3(g(x))$
Plug value of $g(x)$ in the right hand side.
$f(g(x))=3(x-5)$
$f(g(x))=3x-15$.
Hence, $(f\circ g)(x) =3x-15$.
(b) $(g\circ f)(x) = g(f(x))$
Replace $x$ with $f(x)$ in the function $g(x)$.
$g(f(x))=f(x)-5$
Plug value of $f(x)$ in the right hand side.
$g(f(x))=3x-5$.
Hence, $(g\circ f)(x) =3x-5$.
(c) Replace $x$ with $2$ in the part (a) solution.
$(f\circ g)(2) = 3(2)-15$
$(f\circ g)(2) = 6-15$
$(f\circ g)(2) = -9$.
