Answer
(a.)$(f\circ g)(x) =15x-18$.
(b.)$(g\circ f)(x) =15x+2$.
(c.)$(f\circ g)(2) =12$.
Work Step by Step
The given functions are
$f(x)=5x+2$ and $g(x)=3x-4$.
(a) $(f\circ g)(x) = f(g(x))$
Replace $x$ with $g(x)$ in the function $f(x)$.
$f(g(x))=5(g(x))+2$
Plug value of $g(x)$ in the right hand side.
$f(g(x))=5(3x-4)+2$
$f(g(x))=15x-20+2$
$f(g(x))=15x-18$.
Hence, $(f\circ g)(x) =15x-18$.
(b) $(g\circ f)(x) = g(f(x))$
Replace $x$ with $f(x)$ in the function $g(x)$.
$g(f(x))=3(f(x))-4$
Plug value of $f(x)$ in the right hand side.
$g(f(x))=3(5x+2)-4$
$g(f(x))=15x+6-4$.
$g(f(x))=15x+2$.
Hence, $(g\circ f)(x) =15x+2$.
(c) Replace $x$ with $2$ in the part (a) solution.
$(f\circ g)(2) =15(2)-18$
$(f\circ g)(2) =30-18$
$(f\circ g)(2) =12$.
