Inverse hyperbolic cosine function

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This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.
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Definition

The inverse hyperbolic cosine function, denoted \cosh^{-1}, is a function with domain the set [1,\infty), defined in either of the following equivalent ways:

  1. It is the inverse function to the restriction of the hyperbolic cosine function \cosh to the subset [0,\infty).
  2. It is given explicitly by the expression:

\cosh^{-1} x := \ln|x + \sqrt{x^2 - 1}|, \qquad x \ge 1