Answer
a. $(f\circ g)(x)=x$
b. $(g\circ f)(x)=x$
c. $(f \circ g)(3)=3$
d. $(f \circ h)(x)=\log_{2} 4x$
e. $(f\circ h)(8)=5$
Work Step by Step
$f(x)=\log_{2} x, g(x)=2^x, h(x)=4x$
a. $(f\circ g)(x)=\log_{2} {2^x}=x\log_{2} 2=x,$
Domain of $(f\circ g) (x)$ is that $x\in\mathbb{R}$
b.$(g\circ f)(x)=2^{\log_{2} x}=x$
Domain of $(g\circ f )(x)$ is that $x>0$
c. $(f \circ g)(3)=3,$
d. $(f \circ h )(x)=\log_{2} 4x$
Domain of $(f\circ h)(x)$ is that $x>0$
e. $(f\circ h)(8)=\log_{2} {32}=\log_{2} 2^5=5$
