Answer
$a.$ $(f\circ g)(x)=\sqrt{x-1}$
$b.$ $(g\circ f)(x)=\sqrt{x}-1$
$c.$ $(f\circ g)(2)=\sqrt{3}\approx1.7321$
$d.$ $(g\circ f)(2)=\sqrt{2}-1\approx0.4142$
Work Step by Step
$f(x)=\sqrt{x}$ $,$ $g(x)=x-1$
$a.$ $(f\circ g)(x)$
To find $(f\circ g)(x)$, substitute $x$ by $g(x)$ in $f(x)$ and simplify:
$(f\circ g)(x)=f(g(x))=\sqrt{x-1}$
$b.$ $(g\circ f)(x)$
To find $(g\circ f)(x)$, substitute $x$ by $f(x)$ in $g(x)$ and simplify:
$(g\circ f)(x)=g(f(x))=\sqrt{x}-1$
$c.$ $(f\circ g)(2)$
Substitute $x$ by $2$ in $(f\circ g)(x)$, which was found in part $a$, and evaluate:
$(f\circ g)(2)=f(g(2))=\sqrt{2-1}=\sqrt{3}\approx1.7321$
$d.$ $(g\circ f)(2)$
Substitute $x$ by $2$ in $(g\circ f)(x)$, which was found in part $b$, and evaluate:
$(g\circ f)(2)=g(f(2))=\sqrt{2}-1\approx0.4142$
