The hyperbolic sine function, sinh ⁡ ( x ) , is defined by the equation: sinh ⁡ ( x ) = e x − e − x 2 Find a formula for its inverse, sinh − 1 ⁡ ( x )

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The hyperbolic sine function,   sinh  ⁡  (  x  ) , is defined by the equation:  sinh  ⁡  (  x  )  =                    e        x            −              e                  −          x                      2  Find a formula for its inverse,      sinh          −      1        ⁡  (  x  )

humusen6p · Accepted Answer

Let   y  =      sinh          −      1        ⁡  (  x  )  x  =                              e          y                −                  e                      −            y                              2          ⟹        e          2      y        −  2  x      e          y        −  1  =  0    ⟹        e          y        =  x  +            x      2        +    1        ⟹        sinh          −      1        ⁡  (  x  )  =  ln  ⁡  (  x  +            x      2        +    1    )

The hyperbolic sine function, sinh ⁡ ( x ) , is defined by the eq

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