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The domain of the function

f \left ( a \right ) = \frac{1}{\sqrt{\left [ a \right ]^{2} -\left [ a \right ]-6}}

Where \left [ \right ] denotes greater integer function.

  • Option 1)

    R - \left [ -2,4 \right ]

  • Option 2)

    R - \left \{ -3,2 \right \}

  • Option 3)

    R

  • Option 4)

    R - \left \{ 2,3 \right \}

 

Answers (1)

As learnt in concept

Domain of function -

All posible values of x for f(x) to be defined is known as domain.

-

 

 

Greatest Integer Function -

\left [ x \right ]= Greatest integer less than or equal to x

\left ( for\: x\: \in\: R \right )

- wherein

Range = Integers

 

 

 f(a)=\frac{1}{\sqrt{[a]^{2}-[a]-6}}

For domain

[a]^{2}-[a]-6>0

[a]^{2}-3[a]+2[a]-6>0

([a]+2)([a]-3)>0

[a]<-2 or [a]>3

Thus a<-2 or a>4


Option 1)

R - \left [ -2,4 \right ]

This option is correct

Option 2)

R - \left \{ -3,2 \right \}

This option is incorrect

Option 3)

R

This option is incorrect

Option 4)

R - \left \{ 2,3 \right \}

This option is incorrect

Posted by

Vakul

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