Answer
$f(x)=4x-5$ and $g(x)=x+1$ or vice versa.
Work Step by Step
The given expression is
$(fg)(x)=4x^2-x-5$
Factor the right hand side
$4x^2-x-5$
Rewrite $-x$ as $-5x+4x$.
$4x^2-5x+4x-5$
Group terms.
$(4x^2-5x)+(4x-5)$
Factor from each group.
$x(4x-5)+1(4x-5)$
Factor out $(4x-5)$.
$(4x-5)(x+1)$
Plug the above value into the given expression.
$(fg)(x)=(4x-5)(x+1)$
And $(fg)(x)=f(x)\cdot g(x)$.
$f(x)\cdot g(x)=(4x-5)(x+1)$
Hence, $f(x)=4x-5$ and $g(x)=x+1$ or vice versa.
