Final answer:
To find f(2) for the given function, we substitute x=2 in the appropriate expression of the function.
Step-by-step explanation:
The given function is f(x) = {-x–5 for x<1, -(x–7)^2 for x>4}. We need to find f(2).
Since 2 is greater than 1 and less than 4, it falls in the range for which the function is defined as -(x–7)^2. So, we substitute x=2 in -(x–7)^2:
f(2) = -((2-7)^2)
= -(-5^2) = -(-25) = 25