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Question Number 66827 by mr W last updated on 20/Aug/19

Commented by mr W last updated on 20/Aug/19

$t h e g r a p h a b o v e s h o w s t h e e q u a t i o n$ $\frac{\ln (x + \sqrt{1 + x^{2}})}{\sqrt{1 + x^{2}}} = \frac{\ln (y + \sqrt{1 + y^{2}})}{\sqrt{1 + y^{2}}}$ $i t c o n t a i n s i n f a c t t w o c u r v e s :$ $c u r v e 1 : y = x w h i c h a l w a y s f u l f i l l s$ $t h e e q u a t i o n$ $c u r v e 2 : y = ? ? ?$ $c a n y o u f i n d t h e f u n c t i o n f o r c u r v e 2$ $i n f o r m o f y = f (x) ?$ $c a n y o u f i n d t h e i n t e r s e c t i o n p o i n t$ $o f b o t h c u r v e s ? i m e a n w i t h e x a c t$ $v a l u e s ?$
Commented by Prithwish sen last updated on 23/Aug/19

$Sir, is there any process of decomposing$ $such functions ?$
Commented by mr W last updated on 24/Aug/19

$I {d o n}^{'} t k n o w, s i r .$ ${T h a t}^{'} s a l s o m y q u e s t i o n .$ $A f a m o u s e x a m p l e i s x^{y} = y^{x} .$
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