Inverse Hyperbolic Function - Composition of Hyperbolic and Inverse Hyperbolic Functions

Composition of Hyperbolic and Inverse Hyperbolic Functions

\begin{align} &\sinh(\operatorname{arcosh}\,x) = \sqrt{x^{2} - 1} \quad \text{for} \quad |x| > 1 \\ &\sinh(\operatorname{artanh}\,x) = \frac{x}{\sqrt{1-x^{2}}} \quad \text{for} \quad -1 < x < 1 \\ &\cosh(\operatorname{arsinh}\,x) = \sqrt{1+x^{2}} \\ &\cosh(\operatorname{artanh}\,x) = \frac{1}{\sqrt{1-x^{2}}} \quad \text{for} \quad -1 < x < 1 \\ &\tanh(\operatorname{arsinh}\,x) = \frac{x}{\sqrt{1+x^{2}}} \\ &\tanh(\operatorname{arcosh}\,x) = \frac{\sqrt{x^{2} - 1}}{x} \quad \text{for} \quad |x| > 1 \end{align}

Read more about this topic:  Inverse Hyperbolic Function

Famous quotes containing the words composition of, composition, inverse and/or functions:

    “There was not a grain of poetry in the whole composition of Lord Fawn, and poetry was what her very soul craved;Mpoetry, together with houses, champagne, jewels, and admiration.”
    —Anthony Trollope (1815–1882)

    “When I think of God, when I think of him as existent, and when I believe him to be existent, my idea of him neither increases nor diminishes. But as it is certain there is a great difference betwixt the simple conception of the existence of an object, and the belief of it, and as this difference lies not in the parts or composition of the idea which we conceive; it follows, that it must lie in the manner in which we conceive it.”
    —David Hume (1711–1776)

    “The quality of moral behaviour varies in inverse ratio to the number of human beings involved.”
    —Aldous Huxley (1894–1963)

    “One of the most highly valued functions of used parents these days is to be the villains of their children’s lives, the people the child blames for any shortcomings or disappointments. But if your identity comes from your parents’ failings, then you remain forever a member of the child generation, stuck and unable to move on to an adulthood in which you identify yourself in terms of what you do, not what has been done to you.”
    —Frank Pittman (20th century)