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प्रश्न
If f : R → R be given by for all \[f\left( x \right) = \frac{4^x}{4^x + 2}\] x ∈ R, then
विकल्प
(a) f(x) = f(1 − x)
(b) f(x) + f(1 − x) = 0
(c) f(x) + f(1 − x) = 1
(d) f(x) + f(x − 1) = 1
उत्तर
(c) f(x) + f(1 − x) = 1
\[f\left( x \right) = \frac{4^x}{4^x + 2}\]
\[f (1 - x) = \frac{4^{1 - x}}{4^{1 - x} + 2}\]
\[ = \frac{4}{2 \times 4^x + 4}\]
\[ = \frac{2}{4^x + 2}\]
\[f(x) + f(1 - x) = \frac{4^x}{4^x + 2} + \frac{2}{4^x + 2} \]
\[ = \frac{4^x + 2}{4^x + 2} = 1\]
\[\]
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