Question

The function f(x)=15x+8
represents the cost of purchasing x books and having them shipped. The function g(x)=2x+5
represents a discount of $2 per book purchased and a discount of $5 for shipping. What function represents the cost of purchasing x books after the discounts?

Enter the missing values.

(1 point)
The function that represents the cost of purchasing x books after the discounts is $$
.​​​​​​​
Remaining Attempts : 3

Answer 1

To find the cost of purchasing \( x \) books after applying the discounts, we need to subtract the discount function \( g(x) \) from the cost function \( f(x) \).

The functions are given as follows:
- \( f(x) = 15x + 8 \) (the original cost)
- \( g(x) = 2x + 5 \) (the discounts)

To find the total cost after discounts, we can express it as:
\[
\text{Total Cost after Discounts} = f(x) - g(x)
\]

Now we calculate this:
\[
f(x) - g(x) = (15x + 8) - (2x + 5)
\]

Now, simplify the expression:
\[
= 15x + 8 - 2x - 5
\]
\[
= (15x - 2x) + (8 - 5)
\]
\[
= 13x + 3
\]

Thus, the function that represents the cost of purchasing \( x \) books after the discounts is:
\[
\boxed{13x + 3}
\]