Answer
$\color{blue}{\bf{(a) \text{ } g(x)= \dfrac{x}{2} }}$
$\color{blue}{\bf{(b) \text{ } f(x)= x+1 }}$
$\color{blue}{\bf{(c) \text{ } (f \text{ }\omicron\text{ } {g})(x)=
\dfrac{1}{2}x +1 }}$
$\color{blue}{\bf{(d) \text{ } {$}31 }}$
Work Step by Step
The items are on sale for $\dfrac{1}{2}$ the original price $x$, + ${$}1$
$\bf{(a)}$ $g(x)$ is a function for half the price of the original item
$\color{blue}{\bf{ g(x)= \dfrac{1}{2}x }}$
$\bf{(b)}$ $f(x)$ is a function that adds $1$ to x
$\color{blue}{\bf{ f(x)= x+1 }}$
$\bf{(c)}$ $\color{blue}{\bf{(f \text{ }\omicron\text{ } {g})(x)=
\dfrac{1}{2}x +1 }}$
$\bf{(d)}$ To find the sale price of a ${$}60$ item:
$(f \text{ }\omicron\text{ } {g})(60)=\dfrac{1}{2}(60) +1$
$(f \text{ }\omicron\text{ } {g})(60)=30 +1$
$(f \text{ }\omicron\text{ } {g})(60)=$ $\color{blue}{\bf{{$}31 }}$
