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

Answer 1

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