Answer: Undefined
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Explanation:
This is a piecewise function. The f(x) has a "split identity" so to speak.
If [tex]0 \le x < 3[/tex], then [tex]f(x) = x+1[/tex]
OR
If [tex]3 < x \le 6[/tex], then [tex]f(x) = -x+11[/tex]
The f(x) will depend on what the input x is.
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We want to find f(3) which is the value of f(x) when x = 3.
Notice that x = 3 isn't actually part of either inequality mentioned. Both inequalities leave 3 out. The first inequality is smaller than 3; the second one is larger than 3.
Therefore, f(3) is undefined
The graph is shown below. Note the open holes at each endpoint involving x = 3 to indicate those points aren't part of the graph. Think of them as potholes you can't drive on (the curve being the road). This is a visual way to show that f(3) is undefined.
