Mathegoras

Functions › Even, odd and periodic functions › Odd and even functions

Roots of a symmetric odd function

High school · ●●●○○ 50 pts

Let y=f(x)y=f(x) be an odd function defined on R\mathbf{R} whose graph is symmetric about the line x=1x=1. When 0<x≤10<x\leq 1, f(x)=log⁡3xf(x)=\log_3 x. Find the sum of all real roots of the equation f(x)=−13+f(0)f(x)=-\frac{1}{3}+f(0) in the interval (0,10)(0,10).

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odd functionssymmetry of graphsperiodic functionslogarithmssum and product of roots