Answer
a) $L_2$; b) $L_1$; c) $L_4$; d) $L_3$
Work Step by Step
a) $f(p)$: a $50\%$ discount is applied
We notice that $p=10$ corresponds to $S=5$, and $p=15$ corresponds to $S=15$, so $f(p)$ matches $L_2$.
b) $g(p)$: $\$5$ is applied.
We notice that $p=20$ corresponds to $S=15$, and $p=15$ corresponds to $S=10$, so $g(p)$ matches $L_1$.
c) $(g\circ f)(p)$
$(g\circ f)(p)$ matches $L_4$.
d) $(f\circ g)(p)$
We notice that when applying a discount of $\$5$, and then a discount of $509\%$ to $p=20$, we get $S=7.5$, so $(g\circ f)(p)$ matches $L_3$.
