Range of the function f ( x ) = x 2 + x 2 + 1 1 , is

f ( x ) = x 2 + 1 + x 2 + 1 1 − 1 x 2 + 1 + x 2 + 1 1 ≥ 2 [ ∵ AM ≥ GM ] x 2 + x 2 + 1 1 ≥ 1 ∴ f ( x ) ∈ [ 1 , ∞ )

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Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsDomain-RangeEasy2 minQB

MathematicsEasysingle choice

Range of the function $f (x) = x^{2} + \frac{1}{x ^{2} + 1}$ , is

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Solution:

$f (x) = x^{2} + 1 + \frac{1}{x ^{2} + 1} - 1$ $x^{2} + 1 + \frac{1}{x ^{2} + 1} \geq 2 [∵ AM \geq GM] x^{2} + \frac{1}{x ^{2} + 1} \geq 1 ∴ f (x) \in [1, \infty)$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Domain-Range

⏱ 2mℹ️ Source: QB

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