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  4. The minimum value of expression 3x + 31-x, x∈ R, is

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Q. The minimum value of expression $3^{x} + 3^{1-x}, x\in R$, is

Sequences and Series

Solution:

We know that $A.M. \ge G.M$. for positive numbers.
Therefore, $\frac{3^{x}+3^{1-x}}{2} \ge \sqrt{3^{x} \cdot 3^{1-x}}$
$ \Rightarrow 3^{x} + 3^{1-x} \ge 2\sqrt{3}$