well, if m = 1, let's see, then f(x) = √(mx) = √(1x) = √x
and then g(x) = m√x = 1√x = √x
well, if both equations are equal, then their ranges are also equal.
now, if m = "any positive real number"
f(x) = √(mx) = √m √x will yield some value over the y-axis
g(x) = m√x will yield some range over the y-axis, however, "m" is a larger value than "√m".
what that means is that so long "m" is a positive real number, the ranges of f(x) and g(x) will be the same over an infinite range on the y-axis, even though g(x) is moving faster than f(x), f(x) is moving slower because √m makes a stretch transformation which is smaller than one "m" does.