# $f(x) +f^{-1}(x)$

Calculus Level 3
• If $f(a) =a$ and $f(b) =b$, then find the value of $a$ that makes $\int_{a}^{b} [f(x) + f^{-1} (x)]dx = b^2-2a+1$
• [$f(x)$ and $f^{-1}(x)$ are functions]
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