Final answer:
To find (f⋅g)(x), you need to multiply the two given functions, f(x) and g(x), and then simplify the expression obtained.
Step-by-step explanation:
The question asks us to find and simplify the product of two functions, f(x) and g(x), which are given as f(x) = -x + 3 and g(x) = -x - 1.
To find (f⋅g)(x), we need to multiply the two functions:
(f⋅g)(x) = f(x) * g(x) = (-x + 3)*(-x - 1)
We can simplify this expression by applying the distributive property:
(f⋅g)(x) = (-x + 3)*(-x - 1) = -x*(-x) - x*(-1) + 3*(-x) + 3*(-1) = x^2 + x - 3x - 3
Combining like terms, we get:
(f⋅g)(x) = x^2 - 2x - 3