Find the Value of Constant ‘K’ So that the Function F (X) Defined as F(X) = `{((X^2 -2x-3)/(X+1), X != -1),(K, X != -1):}` is Continous at X = -1 - Mathematics

Question

Find the value of constant ‘k’ so that the function f (x) defined as

f(x) = ${\begin{cases} \frac{x^{2} - 2 x - 3}{x + 1} & x \neq - 1 \\ k & x \neq - 1 \end{cases}$

is continous at x = -1

Solution

Given f (x) is continuous at x = -1

$∴ f (- 1) = lim_{x \to - 1} f (x)$

$∴ k = lim_{x \to - 1} \frac{x^{2} - 2 x - 3}{x + 1}$

$= lim_{x \to - 1} \frac{(x - 3) (x + 1)}{x + 1}$ [ $∵ x \to - 1 \Rightarrow x + 1 \neq 0$ ]

= -1-3=-4

∴ K = -4

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Concept of Continuity

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Find the Value of Constant ‘K’ So that the Function F (X) Defined as F(X) = ${\begin{cases} \frac{X^{2} - 2 x - 3}{X + 1} & X \neq - 1 \\ K & X \neq - 1 \end{cases}$ is Continous at X = -1 - Mathematics

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