If $f$ is an even function defined in the interval $(-5,5)$, find the number of real values of $x$ satisfying the equation $$f(x) = f(\frac{x+1}{x+2})$$ I solved it as $$f(x) = f(-x) = f(\frac{x+1}{x+2})$$ $$x = \frac{x+1}{x+2}$$ $$-x = \frac{x+1}{x+2}$$ $$x = \frac{-1±\sqrt5}{2},\frac{-3±\sqrt5}{2}$$ But I saw in many books as $$f(x) = f(-x) = f(\frac{x+1}{x+2})$$ and $$f(x) = f(-x) = f(\frac{-x+1}{-x+2})$$ So, I am confused between these solutions. Could you please tell me which one is correct?
2026-02-23 20:40:51.1771879251
Find the solutions of a functional equation
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