Chapter 12, Problem 6CR

(a)

To determine

The value of function $\left(f\circ g\right)\left(2\right)$, where $f\left(x\right)=\frac{3x}{x-2}$, and $g\left(x\right)=2x+1$.

(b)

To determine

The value of the function $\left(g\circ f\right)\left(4\right)$, where $f\left(x\right)=\frac{3x}{x-2}$, and $g\left(x\right)=2x+1$.

(c)

To determine

The value of the function $\left(f\circ g\right)\left(x\right)$, where $f\left(x\right)=\frac{3x}{x-2}$, and $g\left(x\right)=2x+1$.

(d)

To determine

The domain of $\left(f\circ g\right)\left(x\right)$, where $f\left(x\right)=\frac{3x}{x-2}$, and $g\left(x\right)=2x+1$.

(e)

To determine

The value of the function $\left(g\circ f\right)\left(x\right)$, where $f\left(x\right)=\frac{3x}{x-2}$, and $g\left(x\right)=2x+1$.

(f)

To determine

The domain of $\left(g\circ f\right)\left(x\right)$, where $f\left(x\right)=\frac{3x}{x-2}$, and $g\left(x\right)=2x+1$.

(g)

To determine

The inverse of the function $g$ and its domain, where $g\left(x\right)=2x+1$.

(h)

To determine

The inverse of the function $f$ and its domain, where $f\left(x\right)=\frac{3x}{x-2}$.