Answer
$f(x)=3x-13$ and $g(x)=x-3$ or vice versa.
Work Step by Step
The given expression is
$(fg)(x)=3x^2-22x+39$
Factor the right hand side
$3x^2-22x+39$
Rewrite $-22x$ as $-13x-9x$.
$3x^2-13x-9x+39$
Group terms.
$(3x^2-13x)+(-9x+39)$
Factor from each group.
$x(3x-13)-3(3x-13)$
Factor out $(3x-13)$.
$(3x-13)(x-3)$
Plug the above value into the given expression.
$(fg)(x)=(3x-13)(x-3)$
And $(fg)(x)=f(x)\cdot g(x)$.
$f(x)\cdot g(x)=(3x-13)(x-3)$
Hence, $f(x)=3x-13$ and $g(x)=x-3$ or vice versa.