Question: The minimum value of $f(x)=a^{a^{x}}+a^{1-a^{x}}$ where $\mathrm{a}, \mathrm{x} \in \mathrm{R}$ and $\mathrm{a}>0$, is equal to :
$2 \mathrm{a}$
$2 \sqrt{\mathrm{a}}$
$a+\frac{1}{a}$
$a+1$
Correct Option: , 2
Solution:
A.M. $\geq$ G.M.
$f(x)=a^{a^{x}}+a^{1-a^{x}}=a^{a^{x}}+\frac{a}{a^{a^{x}}} \geq 2 \sqrt{a}$
