Multiple choice general knowledge math & puzzles

If functions f(x) and g(x) are continuous everywhere and f(1) = 2, f(3) = -4, f(4) = 8, g(0) = 4, g(3) = -6 and g(7) = 0 then lim (f + g)(x) as x approaches 3 is equal to

  1. -10

  2. -11

  3. -15

  4. cannot find a value for the above limit since only values of the functions are given.
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A Correct answer
Explanation

Since $f$ and $g$ are continuous everywhere, the limit of their sum as $x$ approaches 3 is simply $f(3) + g(3)$. Given $f(3) = -4$ and $g(3) = -6$, the sum is $-4 + (-6) = -10$. Continuity ensures the limit equals the function value.

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