Question
Sat March 21, 2015 By: Divya Lekha

find the range and domain:
 f(x)=2^x
 f(x)=e^-x
f(x)=1-|x|
f(x)=|x+3|/|x+3|
 
 

Expert Reply
Vimala Ramamurthy
Mon March 23, 2015
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 t h a t space x space c a n space t a k e. 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 t h a t space y space c a n space t a k e. 1. C o n s i d e r space t h e space f u n c t i o n space f open parentheses x close parentheses equals 2 to the power of x H e r e comma space x space c a n space t a k e space a n y space r e a l space v a l u e s space a n d space h e n c e space bold italic R space i s space t h e space d o m a i n space o f space t h e space f u n c t i o n. O b s e r v e 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 a b o v e space f u n c t i o n.
T h u s space r a n g e space o f space f left parenthesis x right parenthesis space i s space t h e space s e t space o f space p o s i t i v e space r e a l space n u m b e r s comma space bold italic R to the power of bold plus
2. C o n s i d e r space t h e space f u n c t i o n space f left parenthesis x right parenthesis equals e to the power of negative x end exponent H e r e comma space x space c a n space t a k e space v a l u e s space f r o m space minus infinity space t o space plus infinity H e n c e space d o m a i 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 bold italic R 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 g r a p h space i t space i s space c l e a r space t h a t space y space c a n space t a k e space v a l u e s space f r o m space infinity space t o space 0 T h u s comma 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 bold italic R to the power of bold plus
3. C o n s i d e r space t h e space g i v e n space f u n c t i o n space f left parenthesis x right parenthesis equals 1 minus open vertical bar x close vertical bar H e r e comma space x space c a n space t a k e space v a l u 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 d o m a i n 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. O b s e r v e space t h e space f o l l o w i n g space g r a p h.
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 y space c a n space t a k e space a space m a x i m u m space v a l u e space o f space 1 T h u s 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 left parenthesis negative infinity comma 1 right square bracket comma space t h a t space i s space y less or equal than 1
 
 
4. question is not clear. Please check your question
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