Choose the correct answer. The minimum value of 4^ x +4^ 1-x ,x i… - Vidyadip

MCQ

Choose the correct answer. The minimum value of $4^{\text{x}}+4^{1-\text{x}},\text{x}\in\text{R}$ is:

A
$2$
✓
$4$
C
$1$
D
$0$

✓

Answer

Correct option: B.

$4$

We know that $\text{AM}\geq\text{GM}$
$\therefore\ \frac{4^\text{x}+4^{1-\text{x}}}{2}\geq\sqrt{4^\text{x}.4^{1-\text{x}}}\Rightarrow4^\text{x}+4^{1-\text{x}}\geq2\sqrt{4^{\text{x}+1-\text{x}}}$
$4^\text{x}+4^{1-\text{x}}\geq2.2\Rightarrow4^\text{x}+4^{1-\text{x}}\geq4$
Hence, the correct option is $(b).$

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