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  • The minimum value of 4^x + 4^1–x, x ∈ R, is A. 2 B. 4 C. 1 D. 0

The minimum value of 4\textsuperscript{x} + 4\textsuperscript{1-x}, x \in R is
A. 2
B. 4
C. 1
D. 0

Answers (1)

The AM-GM inequality states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list   

\\ \frac{x+y}{2} \geq \sqrt {xy} \\\\ \frac{4^{x}+4^{1-x}}{2} \geq \sqrt { \left( 4^{x} \right) \left( 4^{1-x} \right) } \\\\ \frac{4^{x}+4^{1-x}}{2} \geq \sqrt {4} \\\\ 4^{x}+4^{1-x} \geq 4 \\\\

Hence, correct option is b.

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infoexpert21

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