How to solve and draw the graph of this function equation I see a graph of a function equation in the title page of this book, but the specific drawing method is not given in the book. I want to know how to solve this function equation and draw its image:
$$f(x)+f(2x)+f(3x)=0$$

 A: $\newcommand{\bbx}[1]{\,\bbox[15px,border:1px groove navy]{\displaystyle{#1}}\,}
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 \newcommand{\expo}[1]{\,\mathrm{e}^{#1}\,}
 \newcommand{\ic}{\mathrm{i}}
 \newcommand{\mc}[1]{\mathcal{#1}}
 \newcommand{\mrm}[1]{\mathrm{#1}}
 \newcommand{\pars}[1]{\left(\,{#1}\,\right)}
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I guess they ( "the book people" ) chose

*

*An even function.

*Arbitrary definition ( quite old "try and error" method ) in an interval.

*Other values are found with the recurrence.
\begin{align}
\mbox{Namely,}\quad\mrm{f}\pars{x} & =
\left\{\begin{array}{lcl}
\ds{\phantom{-}\mrm{f}\pars{-x}} & \mbox{if} & \ds{x < 0}
\\[2mm]
\ds{\phantom{-}x\sin\pars{63x^{1/7}}} & \mbox{if} & \ds{0 \leq x \leq 1}
\\[2mm]
\ds{-\,\mrm{f}\pars{x \over 3} - \mrm{f}\pars{2x \over 3}}&&\mbox{otherwise}
\end{array}\right.
\end{align}
$\ds{\large\underline{\mbox{The Result}}}:$

