Answer
$a.$ $(f\circ g)(x)=x$
$b.$ $(g\circ f)(x)=x$
$c.$ $(f\circ g)(2)=2$
$d.$ $(g\circ f)(2)=2$
Work Step by Step
$f(x)=6x-3$ $,$ $g(x)=\dfrac{x+3}{6}$
$a.$ $(f\circ g)(x)$
To find $(f\circ g)(x)$, substitute $x$ by $g(x)$ in $f(x)$ and simplify:
$(f\circ g)(x)=f(g(x))=6\Big(\dfrac{x+3}{6}\Big)-3=x+3-3=x$
$b.$ $(g\circ f)(x)$
To find $(g\circ f)(x)$, substitute $x$ by $f(x)$ in $g(x)$ and simplify:
$(g\circ f)(x)=g(f(x))=\dfrac{6x-3+3}{6}=\dfrac{6x}{6}=x$
$c.$ $(f\circ g)(2)$
Substitute $x$ by $2$ in $(f\circ g)(x)$, which was found in part $a$, and evaluate:
$(f\circ g)(2)=f(g(2))=2$
$d.$ $(g\circ f)(2)$
Substitute $x$ by $2$ in $(g\circ f)(x)$, which was found in part $b$, and evaluate:
$(g\circ f)(2)=g(f(2))=2$
