MCQ
Choose the correct answer.
The minimum value of $4^{\text{x}}+4^{1-\text{x}},\text{x}\in\text{R}$ is:
The minimum value of $4^{\text{x}}+4^{1-\text{x}},\text{x}\in\text{R}$ is:
- A2
- B4
- C1
- D0
Solution:
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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