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Joint Entrance Examination
Mathematics
Functions
Question 107
Question 107 of 162
Medium
MCQ
The real valued function \[f(x) = {{\cos e{c^{ - 1}}x} \over {\sqrt {x - [x]} }}\], where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to :
A
all real except integers
B
all non-integers except the interval [ \[-\]1, 1 ]
C
all integers except 0, \[-\]1, 1
D
all real except the interval [ \[-\]1, 1 ]
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Official solution
Domain of \[\cos e{c^{ - 1}}x\] : \[x \in ( - \infty , - 1] \cup [1,\infty )\] and, \[x - [x] > 0\] \[ \Rightarrow \{ x\} > 0\] \[ \Rightarrow x \ne I\] \[ \therefore \] Required domain = \[( - \infty , - 1] \cup [1,\infty ) - I\]
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