Answer
a. $(f\circ g)(6)=\frac{2}{3}$
b. $(g\circ f)(-1)=\sqrt5$
c. $(f\circ f)(5)=\frac{-1}{4}$
d.$(g\circ g)(-2)=2$
Work Step by Step
$f(x)=\frac{x-1}{x},$ $g(x)=\sqrt{x+3}$
a. $(f\circ g)(x)=\frac{\sqrt{x+3}-1}{\sqrt{x+3}}$
Thus, $(f\circ g)(6)=\frac{\sqrt{6+3}-1}{\sqrt{6+3}}=\frac{2}{3}$
b.$(g\circ f)(x)=\sqrt{\frac{x-1}{x}+3}=\sqrt{\frac{4x-1}{x}}$
$(g\circ f)(-1)=\sqrt5,$
c. $(f\circ f)(x)=\frac{\frac{x-1}{x}-1}{\frac{x-1}{x}}=\frac{-1}{x-1},$
$(f\circ f)(5)=\frac{-1}{4}$
d. $(g\circ g)(-2)=\sqrt{\sqrt{-2+3}+3}=\sqrt{1+3}=\sqrt{4}=2$
