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) $(f\circ g)(2)=f(2(2)^2+1)=f(9)=\sqrt {9+2}=\sqrt {11}$.
(b) $(g\circ f)(-2)=g(\sqrt {-2+2})=g(0)=1 $.
(c) $(f\circ f)(4)=f(\sqrt {4+2})=\sqrt {\sqrt 6+2} $.
(d) $(g\circ g)(-1)=g(2(-1)^2+1)=g(3)=2(3)^2+1=19$.
