Asked by joykphukan | 16th Mar, 2015, 07:50: PM

Expert Answer:

G i v e n space t h a t space f open parentheses x close parentheses equals open curly brackets open parentheses x comma fraction numerator x squared over denominator 1 plus x squared end fraction close parentheses colon x element of R close curly brackets S q u a r e space o f space a space r e a l space n u m b e r space i s space p o s i t i v e space a n d space t h e space s u m space o f space a space p o s i t i v e space n u m b e r space a n d space o n e space i s space a l w a y s space p o s i t i v e. A n d space f open parentheses 0 close parentheses equals 0 comma space t h e r e f o r e space t h e space r a n g e space o f space i s space t h e space s e t space o f space r e a l space n u m b e r s space R. C o n s i d e r space t h e space f o l l o w i n g space g r a p h space o f space t h e space g i v e n space f u n c t i o n. F r o m space t h e space g r a p h space i t space i s space c l e a r space t h a t space t h e space r a n g e space o f space t h e space g i v e n space f u n c t i o n space i s space t h e space s e t space o f space r e a l space n u m b e r s. space

Answered by Vimala Ramamurthy | 17th Mar, 2015, 11:18: AM