Question

Find the period of f(x)=sinx+{x}?

Answer 1

`f(x)` is aperiodic

Explanation:

I will assume that by `{x}` you mean the fractional part of `x`, i.e.:

`{x} = x - floor(x)`

This function has period `1` with graph like this:

graph{3/5(abs(sin(xpi/2))-abs(cos(xpi/2))-abs(sin(xpi/2)^3)/6+abs(cos(xpi/2)^3)/6)tan(xpi/2)/abs(tan(x*pi/2))+1/2 [-2.48, 2.52, -0.75, 1.75]}

Meanwhile, the function `sin x` has period `2 pi`

graph{sin x [-20.46, 20.54, -1.24, 1.26]}

Note that `2pi` is an irrational multiple of `1`, and hence these two constituent functions have no common period.