The minimum value of f ( x )= a a x + a 1- a x , where a, x ∈ R and a0, is equal to :

Question

The minimum value of f ( x )= a a x + a 1- a x , where a, x ∈ R and a>0, is equal to : (A) 2 a (B) 2 √ a  (C) a+(1/a) (D) a +1

Tardigrade Admin · Accepted Answer

A.M. ≥ G.M. f(x)=aax+a1-ax =aax+(a/aax) ≥ 2 √a

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 :