Let f : R → 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 :

Engineering

Mathematics

Arithmetic Mean Geometric Mean and Harmonic Mean

Question

Let f : R → R be such that for all x $\in$ R (2^1+x + 2^1–x), f(x) and (3^x + 3^–x) are in A.P., then the minimum value of f(x) is :

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$f (x) = (\frac{2^{1 - x} + 2^{1 + x} + 3^{x} + 3^{- x}}{2})$

Using AM $\geq$ GM

f1(x) $\geq$ 3