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Solve the following.
f(x) = (x² - 9)/(x - 3) is not defined at x = 3. What value should be assigned to f(3) for…
$f(x) = \frac{x^2 - 9}{x - 3}$ is not defined at $x = 3$. What value should be assigned to $f(3)$ for continuity of $f(x)$ at $x = 3$?
Answer
Answer
For $x \neq 3$: $f(x) = \frac{(x-3)(x+3)}{x-3} = x+3$.
$\lim_{x\to3} f(x) = 3+3 = 6$.
For continuity at $x=3$, $f(3)$ must equal this limit.
Hence $f(3) = 6$.
Final answer: $6$