Functions (XII)

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Question

$The function f is continuous and has the property f(f(x))=1-x, then the value of f (\frac{1}{4}) + f (\frac{3}{4}) i s$

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Solution

$Given f(f(x))=1-x, replacing x→f (x) \Rightarrow f (f (f (x))) =1- f (x) \Rightarrow f (1 - x) = 1 - f (x) s u b s t i t u t i n g f r o m g i v e n$
$\Rightarrow f (1 - x) + f (x) = 1 H e n c e, f (\frac{1}{4}) + f (\frac{3}{4}) = 1$

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