How to find the range of a function?

Asked by zsooonns | 10th Sep, 2015, 05:41: PM

Expert Answer:

D o m a i n 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 o f space x comma space t h a t space x space c a n space a s s u m e space t o space g e t space a space r e a l space f u n c t i o n. R a n g e 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 o f space y space t h a t space y space c a n space a s s u m e space t o space g e t space a space r e a l space f u n c t i o n. C o n s i d e r space t h e space f u n c t i o n comma f open parentheses x close parentheses equals fraction numerator x minus 2 over denominator 3 minus x end fraction L e t space y equals f open parentheses x close parentheses equals fraction numerator x minus 2 over denominator 3 minus x end fraction rightwards double arrow 3 y minus x y equals x minus 2 rightwards double arrow x plus x y equals 3 y minus 2 rightwards double arrow open parentheses 1 plus y close parentheses x equals 3 y minus 2 rightwards double arrow x equals fraction numerator 3 y minus 2 over denominator 1 plus y end fraction T h u s comma space f i r s t space w e space s h o u l d space t r y space t o space g e t space t h e space i n v e r s e space o f space t h e space g i v e n space f u n c t i o n. N o w space t h e space i n v e r s 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 x equals f open parentheses y close parentheses equals fraction numerator 3 y minus 2 over denominator 1 plus y end fraction H e r e comma space y space c a n space a s s u m e space a l l space t h e space v a l u e s space e x c e p t space y equals negative 1 comma space sin c e space a t space y equals negative 1 comma space f u n c t i o n space i s space n o t space d e f i n e d. T h e r e f o r e comma space y element of R minus open curly brackets negative 1 close curly brackets T h u s space r a n g e space o f space f space i s space R minus open curly brackets negative 1 close curly brackets T h e space w a y space o f space f i n d i n g space r a n g e space o f space a space f u n c t i o n space d i f f e r s space f r o m space p r o b l e m space t o space p r o b l e m. B u t space o u r space a i m space i s space t o space g e t space t h e space v a l u e s space o f space y comma space w h e r e space t h e space f u n c t i o n space i s space d e f i n e d. I f space y o u space t r y space m o r e space p r o b l e m s space y o u space w i l l space g e t space t h a t space i n space p r a c t i c e.

Answered by Vimala Ramamurthy | 11th Sep, 2015, 11:08: AM

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