Answer
a. $(f\circ g)(x)=x$
b. $(g\circ f)(x)=x$
c. $(f \circ g)(5)=5$
d. $(f \circ h)(x)=2\ln x$
e. $(f\circ h)(e)=2$
Work Step by Step
$f(x)=\ln x, g(x)=e^x, h(x)=x^2$
a. $(f\circ g)(x)=\ln {e^x}=x\ln e=x,$
Domain of $(f\circ g )(x)$ is that $x>0$
b. $(g\circ f)(x)=e^{\ln x}=x$
Domain of $(g\circ f )(x)$ is that $x>0$
c. $(f \circ g)(5)=5$
d. $(f \circ h )(x)=\ln x^2=2\ln x$
Domain of $(f\circ h)(x)$ is that $x>0$
e. $(f\circ h)(e)=2$
