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Question

The function y=x/(1+x2) decreases in the interval

A
(1,1)
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B
(1,)
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C
(,1)
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D
(,)
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Solution

The correct options are
B (1,)
D (,1)
y=x/(1+x2)
y=(1+x2)2xx(1+x2)2=1x2(1+x2)2
Since (1+x2)2>0 for all x
Therefore y<0 for 1x2<0
x>1 or x<1
Therefore, x(,1) or x(1,).
Thus x/(1+x2) decreases in (,1] or [1,).
Ans: B,C

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