f(x) = e^x

Since the function f(x) is monotonically increasing from the domain R ⁺ → R ⁺

∴f(x) is one –one

Range of f(x) = (1,∞) = R ⁺ (codomain)

∴f(x) is onto

∴ f : R ⁺ → R ⁺ : f(x) = e^x is one - one onto.