Let f:R→R be a function such that f(f(x))=x2−x+1 for all x and the – InterviewSolution

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1.	Let f:R→R be a function such that f(f(x))=x2−x+1 for all x and the value of tan−1(f(1))+sec−1(f(1))+cos−1(f(0))+cot−1(f(0)) is equal to aπb where a and b are co-prime. Then the value of a+b is
Answer» Let $f : R \to R$ be a function such that $f (f (x)) = x^{2} - x + 1$ for all $x$ and the value of ${tan}^{- 1} (f (1)) + {sec}^{- 1} (f (1)) + {cos}^{- 1} (f (0)) + {cot}^{- 1} (f (0))$ is equal to $\frac{a π}{b}$ where $a$ and $b$ are co-prime. Then the value of $a + b$ is

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