Chapter 4.1, Problem 58AYU

(a)

To determine

The function $\left(f\circ g\right)\left(x\right)$ for the functions $f\left(x\right)=\frac{ax+b}{cx+d}$ and $g\left(x\right)=mx$.

(b)

To determine

The function $\left(g\circ f\right)\left(x\right)$ for the functions $f\left(x\right)=\frac{ax+b}{cx+d}$ and $g\left(x\right)=mx$.

(c)

To determine

The domain of $f\circ g$ and $g\circ f$ for the functions $f\left(x\right)=\frac{ax+b}{cx+d}$ and $g\left(x\right)=mx$.

(d)

To determine

The conditions for which $f\circ g=g\circ f$ for the given functions $f\left(x\right)=\frac{ax+b}{cx+d}$ and $g\left(x\right)=mx$.