If f x = e x + x - 1 x + x : x ≠ 0 - 1 : x = 0 (where . denotes the greatest integer function), then

Question

If f x = e x + x - 1 x + x : x ≠ 0 - 1 : x = 0 (where . denotes the greatest integer function), then, f x is continuous at x = 0, l i m x → 0 + f x = - 1, l i m x → 0 - f x = 1, l i m x → 0 + f x = 1

MARKS App · Accepted Answer

f x = e x + x - 1 x + x x ≠ 0 - 1 x = 0 l i m x → 0 - f x = l i m x → 0 - e x + x - 1 x + x = e - 1 - 1 - 1 = e - 1 e l i m x → 0 + f x = l i m x → 0 + e x + x - 1 x + x = l i m x → 0 + e x - 1 x = 1 ∵ LHL ≠ RHL at x = 0 ⇒ f x is discontinuous at x = 0

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