Answer
a) $f(x)=0.9x$
b) $g(x)=x−100$
c) $(f$ º $g)(x)=0.9x−90$
$(g$ º $f)(x)=0.9x−100$
$(g$ º $f)(x)$ gives the lowest price.
Work Step by Step
a) To find the price after applying the 10% discount, one needs to calculate 10% of the regular price and subtract it from the whole regular price. Since 10% = 0.1, $f(x)=x−0.1x=0.9x$
b) a \$100 rebate simply subtracts \$100 from the regular price.
c) $(f$ º $g)(x)=f(g(x)=0.9(x−100)=0.9x−90$
$(g$ º $f)(x)=g(f(x))=0.9x−100$
$(f$ º $g)(x)$ will apply the rebate first and then the 10% discount. This will make a 10% discount to the rebate in addition to the regular price of the washing machine. The other way around will preserve the \$100 rebate. Thus, $(g$ º $f)(x)$ gives the lowest price.
