Chapter 4.1, Problem 19AYU

(a)

To determine

The value of $\left(f\circ g\right)\left(4\right)$ for the functions $f\left(x\right)=\left|x\right|$ and $g\left(x\right)=\frac{1}{x^2+1}$.

(b)

To determine

The value of $\left(g\circ f\right)\left(2\right)$ for the functions $f\left(x\right)=\left|x\right|$ and $g\left(x\right)=\frac{1}{x^2+1}$.

(c)

To determine

The value of $\left(f\circ f\right)\left(1\right)$ for the functions $f\left(x\right)=\left|x\right|$ and $g\left(x\right)=\frac{1}{x^2+1}$.

(d)

To determine

The value of $\left(g\circ g\right)\left(0\right)$ for the functions $f\left(x\right)=\left|x\right|$ and $g\left(x\right)=\frac{1}{x^2+1}$.