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The domain of the function f(x)=\sin^{-1}\left [ \frac{x^{2}+1}{2x} \right ]+\frac{1}{\log \left \{ 2-x \right \}}

(where [.] and {.} respectively denote the greatest integer and fractional part function respectively) is

Option: 1

\left \{ x:x\in I\:and \: x\geq 3\right \}
 


Option: 2

\left \{ x:x\in I\:and \: x\leq 4\right \}


Option: 3

\left ( -\infty ,0 \right )\cup \left ( 0,1 \right )

 


Option: 4

\phi \:(empty\: set)


Answers (1)

best_answer

Answer (4) let \:g(x) \sin^{-1}\left [ \frac{x^{2}+1}{2x} \right ],D_g={-1,1}\\ h(x)=\frac{1}{\log{2-x}},D_h=R-I\\ \\ D_g\cap D_h= \phi

 

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vinayak

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