Let f : R [ ] R be such that for all x [ ] R (21+x + 21--x), f(x) and (3x + 3--x) are in A…

Question

Let f : R $$ \to $$ R be such that for all
x $$ \in $$ R
(21+x + 21--x), f(x) and (3x + 3--x) are in
A.P.,
then the minimum value of f(x) is

Accepted Answer

f(x) = $${{2\left( {{2^x} + {2^{ - x}}} \right) + \left( {{3^x} + {3^{ - x}}} \right)} \over 2} \ge 3$$

As we know, A.M > G.M

Solutions · 1