given by ''ƒ''<math>f(''x'') = ''x''<sup>^3</supmath>. This function is clearly injective, but its derivative is 0 at ''<math>x'' = 0</math>, and its inverse is not analytic, or even differentiable, on the whole interval <math>(−-1, 1)</math>. Consequently, if we enlarge the ___domain to an open subset ''<math>G''</math> of the complex plane, it must fail to be injective; and this is the case, since (for example) ''<math>f''(ε&\varepsilon \omega;) = ''f''(ε\varepsilon) </math> (where &<math>\omega; </math> is a [[primitive root of unity|primitive cube root of unity]] and ε<math>\varepsilon</math> is a positive real number smaller than the radius of ''<math>G''</math> as a neighbourhood of <math>0</math>).
