The Range of the function 

f \left ( m \right ) = n^{2}+\frac{1}{n^{2}+1}

  • Option 1)

    \left [ 1,\infty \right )

  • Option 2)

    \left [ 2,\infty \right )

  • Option 3)

    \left [ \frac{3}{2},\infty \right )

  • Option 4)

    None

 

Answers (1)
P Plabita

as learnt in

Relation between AM, GM and HM of two positive numbers -

AM\geqslant GM\geqslant HM

- wherein

Inequality of the three given means.

 

  

We will use AM\geqslant GM

f(m)=n^{2}+1=\frac{1}{n^{2}+1}\ \ \ -1 \geqslant 2-1 \geqslant 1

 


Option 1)

\left [ 1,\infty \right )

This option is correct.

Option 2)

\left [ 2,\infty \right )

This option is incorrect.

Option 3)

\left [ \frac{3}{2},\infty \right )

This option is incorrect.

Option 4)

None

This option is incorrect.

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