Question

Mary has gone into a department store with two coupons. One coupon is good for 20% off of the total not including tax. The other coupon will take $15 off of her pre-tax total. If f(x) = 0.8x calculates the total after the 20% off coupon and g(x) = x – 15 calculates the total after the $15 dollar off coupon, determine g(f(100)). Then describe what g(f(100)) represents in the context of this problem.

Answer 1

Answer:

The value of g(f(100)) is 65.

Step-by-step explanation:

It is given that one coupon is good for 20% off of the total not including tax. The other coupon will take $15 off of her pre-tax total.

The given functions are

$f(x)=0.8x$

$g(x)=x-15$

where, f(x) calculates the total after the 20% off coupon and g(x) calculates the total after the $15 dollar off coupon.

We need to find the value of g(f(100)).

$g(f(x))=g[0.8(x)]$                 $(\because f(x)=0.8x)$

Substitute x=100 in the above function.

$g(f(100))=g[0.8(100)]$

$g(f(100))=g(80)$

Substitute x=80 in function g(x) to find the value of g(f(100)).

$g(f(100))=80-15$                 $(\because g(x)=x-15)$

$g(f(100))=65$

Therefore, the value of g(f(100)) is 65.

g(f(x)) represents the value goods after applying both coupons consecutively.

Therefore, g(f(100)) represents the value of $100 goods after applying both coupons consecutive is 65.