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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.