The function f: R → (−π/2, π/2), given by f(x) = arctan(x) is bijective, since each real number x is paired with exactly one angle y in the interval (−π/2, π/2) so that tan(y) = x (that is, y = arctan(x)).
The function f: R → (−π/2, π/2), defined by f(x) = arctan(x), is bijective because for every real number x, there exists a unique angle y in the interval (−π/2, π/2) such that tan(y) equals x.