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  • The minimum value of , where a, x <img alt="\epsilon" src="https://entrancecorne

The minimum value of f(x) = a^{a^x} + a^{1-a^{x}} , where a, x \epsilon R and a > 0, is equal to :
Option: 1 2a
Option: 2 2 \sqrt{a}
Option: 3 a + \frac{1}{a}
Option: 4 a +1

Answers (1)

best_answer

\\\text { A.M. } \geq \text { G.M. } \\\\ \frac{a^{a^x}+\frac{a}{a^{a^x}}}{2}\geq\sqrt{\left ( a^{a^x} \right )\left ( \frac{a}{a^{a^x}} \right )} \\ \qquad f(x)=a^{a^{x}}+a^{1-a^{x}}=a^{a^{x}}+\frac{a}{a^{a^{x}}} \geq 2 \sqrt{a}

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