Answer
a.) $\sqrt{sin (x)}$
b.) $sin (\sqrt x)$
c.) $\sqrt[4] x$
d.) $sin( sin (x))$
Work Step by Step
If $f(x) = \sqrt x$ and $g(x) = sin (x)$
a.) $f \circ g = f(g(x)) = f(sin (x)) = \sqrt{sin (x)}$
b.) $g \circ f = g(f(x)) = g(\sqrt x) = sin (\sqrt x)$
c.) $f \circ f = f(f(x)) = f(\sqrt x) = \sqrt{\sqrt x} = \sqrt[4] x$
d.) $g \circ g = g(g(x)) = g(sin (x)) = sin( sin (x))$
