If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\begin{cases}x^2,&x\le1\x+2,&x>1\end{cases}), what is (f(1))?

Correct answer: (1)

The direct answer is option A: 1. A function assigns exactly one output to each permitted input. Here the input is x=1. The rule is written in two parts: use x^2 when x≤1, and use x+2 only when x>1. Since 1≤1 is true, the first rule applies. Therefore f(1)=1^2=1. The second rule is not used, because 1 is not greater than 1. Option A is correct because it gives this value. Option B, 3, would come from incorrectly using 1+2, but that rule is reserved for inputs strictly greater than 1. Option C is wrong because a function cannot give two outputs to the same input; the boundary condition selects only the first rule. Option D is wrong because 1 is included in the first case, so the function is defined there. A useful exam cue is to check the equality sign carefully: ≤ includes the boundary, whereas > does not.