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UKMT Senior Mathematical Challenge, 2015

Algebra Difficulty 2.0 Junior Find the answer United Kingdom

Let $f(x) = x + \sqrt{x^2+1} + \dfrac{1}{x - \sqrt{x^2+1}}$ . What is the value of $f(2015)$ ?

(A) $-1$ (B) $0$ (C) $1$ (D) $\sqrt{2016}$ (E) $2015$

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