Question
Tue March 31, 2015 By: Visnunathan Gaurav

if a function is given such that f(x)=2x .then how f(x)=f(y)???

Expert Reply
Prasenjit Paul
Fri April 03, 2015
W e space d o n o t space k n o w space w h e t h e r space f left parenthesis x right parenthesis space equals space f left parenthesis y right parenthesis. I f space w e space h a v e space t o space p r o v e space w h e t h e r space a space f u n c t i o n space i s space o n e minus o n e space o r space n o t. W e space c a n space p r o v e space i t space b y space s h o w i n g space f o r space f left parenthesis x right parenthesis equals f left parenthesis y right parenthesis rightwards double arrow space x equals y comma space t h e space f u n c t i o n space i s space o n e minus o n e. I n space t h i s space c a s e comma space i f space f left parenthesis x right parenthesis equals 2 x space a n d space w e space r e p l a c e space x space b y space y comma space a space d i f f e r e n t space v a r i a b l e. S o comma space f o r space f left parenthesis x right parenthesis space equals space f left parenthesis y right parenthesis rightwards double arrow 2 x equals 2 y rightwards double arrow x equals y therefore t h e space f u n c t i o n space f left parenthesis x right parenthesis space i s space a space o n e minus o n e space f u n c t i o n.
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