Answer
a) $f(x)=0.8x$
b) $g(x)=x-50$
c) $( f$ º $g)(x)=0.8x-40$
$(g$ º $f)(x)=0.8x-50$
$(g$ º$ f)(x)$ gives the lowest price.
Work Step by Step
a) To find the price after applying the 20% discount, one needs to calculate 20% of the regular price and subtract it from the whole regular price. Since 20% = 0.2, $f(x) = x-0.2x=0.8x$
b) a \$50 coupon simply subtracts \$50 from the regular price.
c) $( f$ º $g)(x)=f(g(x) = 0.8(x-50)=0.8x-40$
$(g$ º $f)(x)=g(f(x))=0.8x-50$
Applying the coupon first and then the 20% discount $( f$ º $g)(x)$ will make a 20% discount to the coupon in addition to the regular price of the phone. The other way around will preserve the \$50 coupon. Thus, $(g$ º $f)(x)$ gives the lowest price.
