If f(x)=ln[ x^2+e/x^2+1 ] then range of f(x) is ?

Asked by Kalyanrao Chavan | 6th Jun, 2014, 11:05: PM

Expert Answer:

G i v e n space f left parenthesis x right parenthesis equals ln open parentheses fraction numerator x squared plus e over denominator x squared plus 1 end fraction close parentheses f o r space a n y space v a l u e space o f space x comma space a b o v e space f u n c t i o n space w o r k s. space S o space d o m a i n space i s space a l l space r e a l space n u m b e r s space R  L e t s space r e w r i t e space t h e space a b o v e space f u n c t i o n  f left parenthesis c right parenthesis equals ln open parentheses fraction numerator 1 plus begin display style e over x squared end style over denominator 1 plus begin display style 1 over x squared end style end fraction close parentheses  f o r space a n y space v a l u e space o f space x comma space a b o v e space f u c t i o n space c a n t space c r o s s space t h e space v a l u e space 1. space S o space m a x i m u m space v a l u e space i s space 1. space  W h e n space x space t e n d s space t o space minus infinity space o r space plus infinity v a l u e space o f space f u n c t i o n space i s space 0.  S o space r a n g e space o f space f left parenthesis x right parenthesis equals space left parenthesis space 0 comma 1 space right square bracket space w h e r e space 0 space i s space n o t space i n c l u d e d space a n d space 1 space i s space i n c l u d e d

Answered by Dharma Teja | 7th Jun, 2014, 06:58: PM