Answer
(a.)$(f\circ g)(x) =2x+5$.
(b.)$(g\circ f)(x) =2x+9$.
(c.)$(f\circ g)(2) =9$.
Work Step by Step
The given functions are
$f(x)=x+4$ and $g(x)=2x+1$.
(a) $(f\circ g)(x) = f(g(x))$
Replace $x$ with $g(x)$ in the function $f(x)$.
$f(g(x))=g(x)+4$
Plug value of $g(x)$ in the right hand side.
$f(g(x))=2x+1+4$
$f(g(x))=2x+5$.
Hence, $(f\circ g)(x) =2x+5$.
(b) $(g\circ f)(x) = g(f(x))$
Replace $x$ with $f(x)$ in the function $g(x)$.
$g(f(x))=2(f(x))+1$
Plug value of $f(x)$ in the right hand side.
$g(f(x))=2(x+4)+1$
$g(f(x))=2x+8+1$.
$g(f(x))=2x+9$.
Hence, $(g\circ f)(x) =2x+9$.
(c) Replace $x$ with $2$ in the part (a) solution.
$(f\circ g)(x) =2(2)+5$
$(f\circ g)(x) =4+5$
$(f\circ g)(x) =9$.
