Answer:
-32
Explanation:
To find the product of two functions, (f * g)(x), we need to first compute f(x) and g(x) individually, and then multiply them together. In this case, we have:
f(x) = 2x^2 - 7x + 10
g(x) = 3x + 5
Let's start by evaluating f(x) and g(x) at x = -2:
f(-2) = 2 * (-2)^2 - 7 * (-2) + 10
= 2 * 4 + 14 + 10
= 8 + 14 + 10
= 32
g(-2) = 3 * (-2) + 5
= -6 + 5
= -1
Now, we can find the product (f * g)(x) by multiplying f(x) and g(x):
(f * g)(x) = f(x) * g(x)
(f * g)(-2) = f(-2) * g(-2)
= 32 * (-1)
= -32
So, the value of (f * g)(-2) is -32.