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Question

The function f(x)=|x1|x2 is monotonically decreasing on

A
(1,)
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B
(0,2)
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C
(0,1)
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D
(2,)
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Solution

The correct options are
C (0,1)
D (2,)
f(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪(x1)x2x<1(x1)x2x1f(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪(x2)x3x<1(x2)x3x1
x<1, if f(x)<0 (for f(x) to be monotonically decreasing
(x2)x3<0x(0,2)
But x<1x(0,1)
For x1, if f(x)<0(x2)x3<0(x2)x3>0x(,0)(2,)
But, x1x(2,)
Hence, x(0,1)(2,)

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