Answer: To find the value of (gof)(-2), we need to substitute -2 into the function gof(x).
First, let's find the value of f(-2) by substituting -2 into the function f(x):
f(x) = 2x² + 4x + 2
f(-2) = 2(-2)² + 4(-2) + 2
f(-2) = 2(4) - 8 + 2
f(-2) = 8 - 8 + 2
f(-2) = 2
Now that we have the value of f(-2), we can substitute it into the function g(x):
g(x) = 2x - 7
g(f(-2)) = 2(2) - 7
g(f(-2)) = 4 - 7
g(f(-2)) = -3
Therefore, the value of (gof)(-2) is -3.
In summary:
- First, we found the value of f(-2) by substituting -2 into the function f(x). I found that f(-2) = 2.
- Then, we substituted the value of f(-2) into the function g(x) to find the value of g(f(-2)). I found that g(f(-2)) = -3.