Let f(x)=ex, g(x)=3x−2  be two functions from R→R . The domain of the function (gof)−1  is

f(x)=ex, g(x)=3x−2 , then f:R→R+, g:R→R ∴ gof:​ R→R  is defined and given by(gof)(x)=g(f(x))=g(ex)=3ex−2 Clearly, gof  is one-one but not ontoWhen x→−∞, 3ex−2→−2             x→∞, 3ex−2→+∞  and ex  is increasing function∴  Range gof=(−2,∞) ∴ gof=R→(−2,∞)  is one-one onto⇒  Domain (gof)−1=(−2,∞) .