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$10. Find f(x) + f(1-x) if f(x) = \frac{a}{a^{x} + \sqrt{a}}$

Hi,

f (x) = \frac{a}{a^{x} + \sqrt{a}} f (1 - x) = \frac{a}{a^{1 - x} + \sqrt{a}} = \frac{a}{\frac{a}{a^{x}} + \sqrt{a}} = \frac{a \times a^{x}}{a + a^{x} \sqrt{a}} = \frac{a \times a^{x}}{(\sqrt{a} + a^{x}) \sqrt{a}} = \frac{\sqrt{a} \times a^{x}}{(\sqrt{a} + a^{x})} f (x) + f (1 - x) = \frac{a}{a^{x} + \sqrt{a}} + \frac{\sqrt{a} \times a^{x}}{(\sqrt{a} + a^{x})} = \frac{a + \sqrt{a} \times a^{x}}{a^{x} + \sqrt{a}} = \frac{(\sqrt{a} + a^{x}) \sqrt{a}}{a^{x} + \sqrt{a}} = \sqrt{a}

Regards

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