Definition:Inverse Hyperbolic Sine/Real

Definition
From Hyperbolic Sine is Bijection over Reals and Inverse of Bijection, we have that $\sinh$ admits an inverse function over $\R$.

So from Domain of Bijection is Codomain of Inverse and Codomain of Bijection is Domain of Inverse, we have that the domain and image of hyperbolic sine over $\R$, is $\R$.

Also see

 * Definition:Inverse Hyperbolic Cosine/Real Domain
 * Definition:Inverse Hyperbolic Tangent/Real Domain
 * Definition:Inverse Hyperbolic Cotangent/Real Domain
 * Definition:Inverse Hyperbolic Secant/Real Domain
 * Definition:Inverse Hyperbolic Cosecant/Real Domain