Final answer:
Upon calculating f(g(x)) and g(f(x)), neither composition resulted in an identity function (just 'x'), which indicates that the functions f(x) = 2x + 11 and g(x) = -x + 2 are not inverses of each other. Therefore, the answer is B. No.
Step-by-step explanation:
The question requires us to use function composition to determine if the functions f(x) = 2x + 11 and g(x) = -x + 2 are inverses of each other. To do this, we will compose one function with the other in both possible orders, meaning we will calculate f(g(x)) and g(f(x)). If both compositions result in the identity function (that is, f(g(x)) = x and g(f(x)) = x), then the functions are indeed inverses of each other.
Let's start by calculating f(g(x)):
- f(g(x)) = f(-x + 2)
- f(g(x)) = 2(-x + 2) + 11
- f(g(x)) = -2x + 4 + 11
- f(g(x)) = -2x + 15
Now, let's calculate g(f(x)):
- g(f(x)) = g(2x + 11)
- g(f(x)) = -(2x + 11) + 2
- g(f(x)) = -2x - 11 + 2
- g(f(x)) = -2x - 9
Neither f(g(x)) nor g(f(x)) resulted in just x, so the functions are not inverses of each other. Therefore, the answer is B. No.