Asked by ligas
Show that sinh (sinh^-1 x) = x
Answers
Answered by
Steve
that is the definition of an inverse function. For any f(x),
f(f^-1(x)) = x
f^-1(f(x)) = x
if f is single-valued, which sinh(x) is.
If you take sinh^-1 of both sides, you have
sinh^-1(sinh(sinh^-1(x))) = sinh^-1(x)
but that only helps if you already know that sinh^-1(sinh(u)) = u.
f(f^-1(x)) = x
f^-1(f(x)) = x
if f is single-valued, which sinh(x) is.
If you take sinh^-1 of both sides, you have
sinh^-1(sinh(sinh^-1(x))) = sinh^-1(x)
but that only helps if you already know that sinh^-1(sinh(u)) = u.