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The minimum value of $f(x) = a^{ax} + a^{1-ax}$, where $a, x \in R$ and $a > 0$, is equal to:
(1) $a + \frac{1}{a}$
(2) $a + 1$
(3) $2a$
(4) $2\sqrt{a}$
AM $\geq$ GM
$\frac{a^{ax} + a^{1-ax}}{2} \geq (a^{ax} \cdot a^{1-ax})^{1/2} \Rightarrow a^{ax} + a^{1-ax} \geq 2\sqrt{a}$
BETA
