Question

If a function f has an inverse, and f(−2)=5, what is f(5)^−1?

A) -2
B) 5
C) 2
D) It cannot be determined from the given information

Answer 1

To determine f(5)^{-1}, we interpret it as finding the value for which the function f gives 5. Since we are told that f(-2) = 5, the inverse would naturally give us the original input when we apply it to the output, hence f^{-1}(5)= -2, making the correct answer A) -2.

Step-by-step explanation:

To find the value of f(5)^{-1}, we need to understand the concept of an inverse function.

If function f has an inverse, then for every pair (x, y) such that f(x) = y, the inverse function f^{-1}(y) = x. In this case, we are given that f(-2) = 5, which means that f^{-1}(5)= -2.

The notation f(5)^{-1} is actually asking for the inverse of the function evaluated at 5, which is equivalent to f^{-1}(5). Therefore, the mentioned correct answer in the final answer is A) -2.