f(x) should be one one f(x) is onto anyway, only one one nature is problem..., so it should be monotonic
since if it is not monotonic, and decides to change its slope, it will be repeating its values
f(x) = ax+cosx
f'(x) = a-sinx > 0 or a-sinx <0 for all x
either a >= 1 or a =<1
since if a = 1, it will be increasing, but not STRICTLY increasing. this is acceptable.