Which of the following hyperbolic functions is the mirror image of their corresponding inverse hyperbolic functions along the line $y = x$ ?

Sine function

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Tangent function

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Cosecant function

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Cosine function for

x \leq 0

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Solution

The correct options are
A Sine function
B Tangent function
C Cosecant function

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Similar questions

Q. Domain and Range of the inverse hyperbolic sine function is R.

There are six trigonometric and six inverse trigonometric functions. Similarly there are six hyperbolic function defined as follows:
The quantity

\frac{e^{x} - e^{- x}}{2}

where

x ϵ R

is called hyperbolic sine of

x

and is written as

sinh x

cosh x = \frac{e^{x} + e^{- x}}{2}

called as hyperbolic cos

x

and hyperbolic tan of

x

is written as

tanh x = \frac{sinh x}{cosh x}

cosech x = \frac{1}{sinh x}, coth x = \frac{1}{tanh x}

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Which of the following hyperbolic functions is the mirror image of their corresponding inverse hyperbolic functions along the line y=x ?

The correct options are A Sine function B Tangent function C Cosecant function

Which of the following hyperbolic functions is the mirror image of their corresponding inverse hyperbolic functions along the line $y = x$ ?

The correct options are
A Sine function
B Tangent function
C Cosecant function