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Solve the following.
Find the value of constant ‘k’ so that the function defined as: is continuous at .
Find the value of constant ‘k’ so that the function $f(x)$ defined as:
$f(x) = \begin{cases} \frac{x^2 - 2x - 3}{x + 1}, & x \ne -1 \\ k, & x = -1 \end{cases}$
is continuous at $x = -1$.
Answer
Answer
AIFor $x \ne -1$: $f(x) = \frac{(x-3)(x+1)}{x+1} = x - 3$.
$\lim_{x\to -1} f(x) = -1 - 3 = -4$.
For continuity at $x=-1$: $f(-1) = \lim_{x\to -1} f(x)$, so $k = -4$.
Final answer: $-4$
From ISC 2018 Mathematics Paper 1, question 1(v).