Spivak Calculus, Ch. 4 Graphs, Problem 18

No, it is not. Why would $\frac12\{2x\}=\{x\}$? For instance, $\left\{\frac12\right\}=\frac12$, whereas you $\frac12\left\{2\times\frac12\right\}=\frac12\{1\}=0$.

It follows from this that you also do not have $\{2x\}=2\{x\}$.

$\{nx\}$ would have a higher frequency (by order n) than $\{x\}$ and have the same amplitude.

$n\{x\}$ would have higher amplitude but the same frequency.

$f(x) = {x} + \frac 12 {2x} + \frac 14 \{4x\}$

Break the domain up into intervals that are $\frac 18$ unit large. Every time you cross an interval, at least one wave will flip from being a positive to a negative contributor to the slope.