Answer
The answer is
$f(g(x))=4x^2-2x-6$.
$g(f(x))=2x^2+10x-3$.
Work Step by Step
The given functions are
$f(x)=x^2+5x$ and $g(x)=2x-3$
For $f(g(x))$ replace $x$ with $g(x)$ in the first function.
$f(g(x))=(g(x))^2+5(g(x))$
Now substitute the value of $g(x)$ from second function.
$f(g(x))=(2x-3)^2+5(2x-3)$
Clear parentheses.
$f(g(x))=4x^2+9-2\cdot 2x\cdot 3+10x-15$
$f(g(x))=4x^2+9-12x+10x-15$
Simplify.
$f(g(x))=4x^2-2x-6$.
For $g(f(x))$ replace $x$ with $f(x)$ in the second function.
$g(f(x))=2(f(x))-3$
Now substitute the value of $f(x)$ from the first function.
$g(f(x))=2(x^2+5x)-3$
$g(f(x))=2x^2+10x-3$.
