To analyze the question, we need to first clarify what it means for a function to produce a specific output for a given input. In this case, we have a function f such that when the input is 1, the output is 5.
This means that f(1) = 5. However, we must consider other possible values of the function at different points and whether certain statements related to this function could hold true or not. Here are some possibilities:
- Option A: f(1) = 5 and f(2) = 5 – This could be true. Functions can have the same output for different inputs.
- Option B: f(1) = 4 – This could not be true since we established that f(1) must equal 5.
- Option C: f(x) is a constant function equal to 5 for all x – This is also possible, as constant functions return the same output regardless of the input.
- Option D: f(1) is undefined – This cannot be true if we are given that f(1) = 5.
Based on this breakdown, we can conclude:
The statement that f(1) = 4 could not be true, as it directly contradicts the information we have about the function f.