First slide

Functions (XII)

Question

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

Moderate

A

(–∞, ∞)
B

R – {0}
C

R
D

None of these

Solution

We have, $y = \frac{e^{- x}}{1 + [x]}$
⇒ (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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