Answer
$(f\circ g)(x)=25x^{2}+1$
$(g\circ f)(x)=5x^{2}+5$
Work Step by Step
$f(x)=x^{2}+1;$ $g(x)=5x$
$(f\circ g)(x)$
To find $(f\circ g)(x)$, substitute $x$ by $g(x)$ in $f(x)$ and simplify:
$(f\circ g)(x)=f(g(x))=(5x)^{2}+1=25x^{2}+1$
$(g\circ f)(x)$
To find $(g\circ f)(x)$, substitute $x$ by $f(x)$ in $g(x)$ and simplify:
$(g\circ f)(x)=g(f(x))=5(x^{2}+1)=5x^{2}+5$
