The minimum value of f x = a a x + a 1 - a x , where a , x ∈ R and a > 0 , is equal to:

A . M . ≥ G . M . f x = a a x + a 1 - a x = a a x + a a a x ≥ 2 a

Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityMedium2 minPYQ_2021

MathematicsMediumstatement

The minimum value of $f (x) = a^{a^{x}} + a^{1 - a^{x}}$ , where $a, x \in R$ and $a > 0$ , is equal to:

Answer:

Solution:

$A . M . \geq G . M .$

$f (x) = a^{a^{x}} + a^{1 - a^{x}} = a^{a^{x}} + \frac{a}{a^{a^{x}}} \geq 2 \sqrt{a}$

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Means / inequality

⏱ 2mℹ️ Source: PYQ_2021

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