Final answer:
To find the value of (f g)(-2), substitute -2 into g and then substitute the result into f. Since f(-2) = 3 and g(-2) = -8, the value of (f g)(-2) is 3.
Step-by-step explanation:
To find the value of (f g)(-2), we need to evaluate the composition of the functions f and g at x = -2. The composition of two functions, f and g, denoted as (f g)(x), is defined as f(g(x)). In this case, (f g)(-2) means we are substituting -2 into g and then substituting the result into f.
Given that g(-2) = -8, we can substitute -2 into g to get g(-2) = -8. Now, we substitute -8 into f to get f(-8). Since we know that f(-2) = 3, we can determine the value of f(-8) by evaluating the same function at the different input.
Therefore, (f g)(-2) = f(g(-2)) = f(-8) = 3.