1. Tardigrade
  2. Question
  3. Mathematics
  4. The minimum value of f ( x )= a a x + a 1- a x , where a, x ∈ R and a>0, is equal to :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

JEE MainJEE Main 2021Sequences and Series

Solution:

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