Hello,How to solve the equation ?
\(\displaystyle f(x)=\sqrt{f(x^2 )}\) .
Why? That doesn't seem to be implied.1) If \(\displaystyle f(x)\in \mathbb R\), then we get the equation \(\displaystyle f(x)=|f(x)|\)
Hello,Why? That doesn't seem to be implied.
Hello,How to solve the equation ?
\(\displaystyle f(x)=\sqrt{f(x^2 )}\) .
Hello,Let's assume that the function is from $\mathbb{R}$ to $\mathbb{R}$.
As $f(0)$ is 0 or 1, one can combine either of those possibilities with a definition of $f(x)$ for other values of $x$. For example, $f(x) = 0$ or $f(x) = |x|^r$, where $r$ is a real number.
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