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Question

The set of values of x for which the function ​​f(x)=log(x25x+6x2+x+1)+1[x21] is defined, is
(where [.] denotes the greatest integer function)

A
(,2]
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B
(2,)
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C
(3,)
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D
(,2)
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Solution

The correct option is C (3,)
f(x)=log(x25x+6x2+x+1)+1[x21]
For f(x) to be defined,
x25x+6x2+x+1>0
x25x+6>0 [x2+x+1>0 xR]
(x2)(x3)>0
x(,2)(3,) ...(1)

Also, 1[x21]0 and [x21]0
[x21]>0
x211
x220
x(,2][2,) ...(2)
From (1) and (2), we have
x(,2][2,2)(3,)

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