Question:
The minimum value of $f(x)=a^{a^{x}}+a^{1-a^{x}}$, where $a, x \in R$ and $a>0$, is equal to:
Correct Option: , 4
Solution:
$\mathrm{AM} \geq \mathrm{GM}$
$\frac{\mathrm{a}^{\mathrm{ax}}+\frac{\mathrm{a}}{\mathrm{anx}}}{2} \geq\left(\mathrm{a}^{\mathrm{ax} \cdot} \frac{\mathrm{a}}{\mathrm{a}^{\mathrm{ax}}}\right)^{1 / 2} \Rightarrow \mathrm{a}^{\mathrm{ax}}+\mathrm{a}^{1-\mathrm{ax}} \geq 2 \sqrt{\mathrm{a}}$
