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

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.

Exams
Articles
Questions