Sir ,as per my knowledge range of f(x) =1 +x^2+x^3 is R-{0} please cleare my dougth 

Asked by Kalyanrao Chavan | 31st May, 2014, 11:35: PM

Expert Answer:

T h e space r a n g e space o f space f open parentheses x close parentheses equals 1 plus x squared plus x cubed space i s space t h e space s e t space o f space a l l space v a l u e s space t h a t space f open parentheses x close parentheses space c a n space t a k e. A t space x equals 0 comma space y equals f open parentheses 0 close parentheses equals 1 plus 0 squared plus 0 cubed equals 1. H e n c e space y space a s s u m e s space f o r space a l l space v a l u e s space o f space x space i n c l u d i n g space x equals 0. T h u s space t h e space r a n g e space o f space f open parentheses x close parentheses space i s space t h e space s e t space o f space r e a l space space n u m b e r s. L e t space u s space o b s e r v e space t h e space f o l l o w i n g space f i g u r e.
F r o m space t h e space f i g u r e comma space i t space i s space c l e a r space t h a t space y space v a r i e s space f r o m space minus infinity space t o space plus infinity. H e n c e space t h e space r a n g e space o f space f space i s space t h e space s e t space o f space a l l space r e a l space n u m b e r s.

Answered by Vimala Ramamurthy | 1st Jun, 2014, 12:52: PM