Answer
(a) $ \sqrt {11}$
(b) $ 1$
(c) $ \sqrt {\sqrt 6+2}$
(d) $ 19$
Work Step by Step
Given $f(x)=\sqrt {x+2}$ and $g(x)=2x^2+1$, we have
(a) $(f\circ g)(2)=f(g(2))=f(2(2)^2+1)=f(9)=\sqrt {9+2}=\sqrt {11}$
(b) $(g\circ f)(-2)=g(f(-2))=g(\sqrt {-2+2})=g(0)=2(0)^2+1=1$
(c) $(f\circ f)(4)=f(f(4))=f(\sqrt {4+2})=f(\sqrt 6)=\sqrt {\sqrt 6+2}$
(d) $(g\circ g)(-1)=g(g(-1))=g(2(-1)^2+1)=g(3)=2(3)^2+1=19$