Chapter 4.5, Problem 85AYU

(a)

To determine

The value of $\left(fog\right)\left(x\right)$ and the domain of $fog$ if $f\left(x\right)=\ln x,g\left(x\right)=e^x$ and $h\left(x\right)=x^2$.

(b)

To determine

The value of $\left(gof\right)\left(x\right)$ and the domain of $gof$ if $f\left(x\right)=\ln x,g\left(x\right)=e^x$ and $h\left(x\right)=x^2$.

(c)

To determine

The value of $\left(fog\right)\left(5\right)$ if $f\left(x\right)=\ln x,g\left(x\right)=e^x$ and $h\left(x\right)=x^2$

(d)

To determine

The value of $\left(foh\right)\left(x\right)$ and the domain of $foh$ if $f\left(x\right)=\ln x,g\left(x\right)=e^x$ and $h\left(x\right)=x^2$.

(e)

To determine

The value of $\left(foh\right)\left(e\right)$ if $f\left(x\right)=\ln x,g\left(x\right)=e^x$ and $h\left(x\right)=x^2$.