#### Question

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

#### Solution

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

`:. f(-1) = lim_(x->-1) f(x)`

`:. k = lim_(x-> -1) (x^2 - 2x -3)/(x+1)`

`= lim_(x->-1) ((x-3)(x+1))/(x+1)` [`∵ x-> -1 => x + 1 != 0`]

= -1-3=-4

∴ K = -4

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#### APPEARS IN

Solution 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 Concept: Concept of Continuity.