Final answer:
The composition (fog)(-2) for the given functions f(x) = 2x + 1 and g(x) = x - 3 is found by first evaluating g at -2, which is -5, and then using this result as the input for f, resulting in f(-5) = -9.
Step-by-step explanation:
To find the composition (f \circ g)(-2), which is read as "f of g of -2", we first evaluate g at -2 and then use that result as the input for the function f.
First, we determine g(-2):
g(x) = x - 3
g(-2) = (-2) - 3 = -5
Now we take the result from g(-2) and plug it into f:
f(x) = 2x + 1
f(g(-2)) = f(-5) = 2(-5) + 1 = -10 + 1 = -9
Therefore, the composition (f \circ g)(-2) equals -9.