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The range of the function $y = \frac{e^{- x}}{1 + [x]} is$

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(–∞, ∞)

R – {0}

None of these

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Correct option is B

We have, y=e−x1+[x]⇒ (1 + [x])y = e–x > 0⇒ (1 + [x])y > 0⇒ y > 0 if 1 + [x] > 0 and y < 0 if 1 + [x] < 0∴ y ∈ R – {0}

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The range of the function y=e−x1+[x] is

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The range of the function $y = \frac{e^{- x}}{1 + [x]} is$