Answer
a. see explanations.
b. $0.6x-5$, see explanations.
c. $0.6(x-5)$, see explanations.
d. $(f\circ g)(x)$, see explanations.
Work Step by Step
a. Given $x$ as the price of a pair of jeans, we can describe $f(x)=x-5$ as: the price of a pair of jeans after a $5$ dollar discount. Similarly, we can describe $g(x)=0.6x$ as the price of a pair of jeans after a $40\%$ discount.
b. We can find $(f\circ g)(x)=0.6x-5$, which means a $40\%$ discount followed by a $5$ dollar discount.
c. We can find $(g\circ f)(x)=0.6(x-5)$, which means a $5$ dollar discount followed by a $40\%$ discount.
d. As $(f\circ g)(x)-(g\circ f)(x)=-5+3=-2$, the composite $(f\circ g)(x)$ has a bigger discount (lower price).
