Chapter 1.2, Problem 12E

(a).

To determine

The function $y=2x-3$ as a composition involving one or more of functions $f,g,h,$ and $j$ if $f\left(x\right)=x-3$, $g\left(x\right)=\sqrt{x}$, $h\left(x\right)=x^3$, and $j\left(x\right)=2x$.

(b).

To determine

The function $y=x^{3/2}$ as a composition involving one or more of functions $f,g,h,$ and $j$ if $f\left(x\right)=x-3$, $g\left(x\right)=\sqrt{x}$, $h\left(x\right)=x^3$, and $j\left(x\right)=2x$.

(c).

To determine

The function $y=x^9$ as a composition involving one or more of functions $f,g,h,$ and $j$ if $f\left(x\right)=x-3$, $g\left(x\right)=\sqrt{x}$, $h\left(x\right)=x^3$, and $j\left(x\right)=2x$.

(d).

To determine

The function $y=x-6$ as a composition involving one or more of functions $f,g,h,$ and $j$ if $f\left(x\right)=x-3$, $g\left(x\right)=\sqrt{x}$, $h\left(x\right)=x^3$, and $j\left(x\right)=2x$.

(e).

To determine

The function $y=2\sqrt{x-3}$ as a composition involving one or more of functions $f,g,h,$ and $j$ if $f\left(x\right)=x-3$, $g\left(x\right)=\sqrt{x}$, $h\left(x\right)=x^3$, and $j\left(x\right)=2x$.

(f).

To determine

The function $y=\sqrt{x^3-3}$ as a composition involving one or more of functions $f,g,h,$ and $j$ if $f\left(x\right)=x-3$, $g\left(x\right)=\sqrt{x}$, $h\left(x\right)=x^3$, and $j\left(x\right)=2x$.