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Question

Let y={(2x2x+1)(11+x)(2x+1x3+1)}

The solution set of x for which y is real is the union of

A
an open set and a closed set
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B
two open sets
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C
two closed sets
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D
a constant and an open set
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Solution

The correct option is A an open set and a closed set
We have,
y={(2x2x+1)(11+x)(2x+1x3+1)}
= {2+2xx2+x12x1(x3+1)}= {(xx2)(x3+1)}
Since, y takes real values
x(1x)(x+1)(x2x+1)0x(1x)(x+1){(x12)2+34}0x(1x)(x+1)0x(1x)x+10
x(,1)[0,1]

263372_140720_ans_aeb1282b3c4b4653ab1353f71ce009c6.png

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