Answer
$a.\quad(f\circ g)(1) = 4$
$b.\displaystyle \quad(g\circ f)(1) = \frac{13}{2}$
$c.\quad (f\circ g)(x) = \sqrt{\dfrac{13+3x}{x}} $
$d.\displaystyle \quad (g\circ f)(x) = \frac{13}{\sqrt{x+3}}$
Work Step by Step
$(f\circ g)(x)=f[g(x)]=\sqrt{g(x)+3}$
$= \sqrt{\frac{13}{x}+3}$
$= \sqrt{\dfrac{13+3x}{x}} \qquad ... \quad(c)$
$(f\circ g)(1)= \sqrt{\frac{13+3}{1}} =\sqrt{16}=4 \qquad ... \quad(a)$
$(g\displaystyle \circ f)(x)=g[f(x)]=\frac{13}{f(x)}$
$= \displaystyle \frac{13}{\sqrt{x+3}} \qquad ... \quad(d)$
$(g\displaystyle \circ f)(1)= \frac{13}{\sqrt{1+3}} =\frac{13}{2} \qquad ... \quad(b)$
