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  4. The minimum value of 4x+41-x, x ∈ R is

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Q. The minimum value of $4^{x}+4^{1-x}, x \in R$ is

Solution:

A. $M \geq G \cdot M$
$\Rightarrow \frac{4^{x}+4^{1-x}}{2} \geq \sqrt{4^{x} \cdot 4^{1-x}}$
$\frac{4^{x}+4^{1-x}}{2} \geq \sqrt{4^{x} \cdot \frac{4}{4^{x}}}$
$ \Rightarrow 4^{x}+4^{1-x} \geq 4$