Find a function f whose arc length from 0 to x is 2x full solution?

Answer 1

One way to do this is to draw a straight line between points that have x-coordinates "0" and "x". Use the Pythagorean theorem to calculate the difference in the y-coordinates, required to get the desired length.

Answer 2

There are infinitely many possible solutions. f(x) =2 for all x is one such. It can depend on whether the function is linear (a straight line) or whether it zigzags between two values - and if so, how many times.