Final answer:
To answer the student's question, the product (f·g)(x) is found by multiplying the functions, resulting in -5x² - 50x - 40, and for x=1, (f·g)(1) is calculated to be -95.
Step-by-step explanation:
The student asks to find the product of two functions f(x) = -5x - 4 and g(x) = x + 10, which is denoted as (f · g)(x), and to evaluate this product when x equals 1, which is (f · g)(1).
To find (f · g)(x), we multiply the two functions:
(f · g)(x) = f(x) · g(x)
= (-5x - 4) · (x + 10)
= -5x² - 50x - 40.
To find (f · g)(1), we substitute x with 1 in the product:
(f · g)(1) = -5(1)² - 50(1) - 40
= -5 - 50 - 40
= -95.