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Asked by g_archanasharma | 05 Apr, 2019, 15:39: PM
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G i v e n colon space f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line S o 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 space i. e. space x element of straight real numbers N o w comma space f left parenthesis x squared right parenthesis equals vertical line x squared minus 1 vertical line space a n d space left square bracket f left parenthesis x right parenthesis right square bracket squared equals left parenthesis vertical line x minus 1 vertical line right parenthesis squared S o comma space f left parenthesis x squared right parenthesis not equal to left square bracket f left parenthesis x right parenthesis right square bracket squared C o n s i d e r comma space f left parenthesis vertical line x vertical line right parenthesis equals vertical line vertical line x vertical line minus 1 vertical line space a n d space vertical line f left parenthesis x right parenthesis vertical line equals vertical line vertical line x minus 1 vertical line vertical line equals vertical line x minus 1 vertical line equals f left parenthesis x right parenthesis N o w space i n space f left parenthesis vertical line x vertical line right parenthesis comma space vertical line x vertical line space w i l l space a l w a y s space r e m a i n space p o s i t i v e space S o space vertical line vertical line x vertical line minus 1 vertical line space w i l l space a l w a y s space g r e a t e r space t h a n space 1 W h e r e a s space i n space vertical line f left parenthesis x right parenthesis vertical line comma space vertical line x minus 1 vertical line space w i l l space a l w a y s space g r e a t e r space t h a n space 0 T h u s comma space f left parenthesis vertical line x vertical line right parenthesis not equal to vertical line f left parenthesis x right parenthesis vertical line C o n s i d e r comma space f left parenthesis x plus y right parenthesis equals vertical line x plus y minus 1 vertical line A n d space f left parenthesis x right parenthesis plus f left parenthesis y right parenthesis equals vertical line x minus 1 vertical line plus vertical line y minus 1 vertical line not equal to vertical line x plus y minus 1 vertical line equals f left parenthesis x plus y right parenthesis H e n c e comma space n o n e space o f space t h e space o p t i o n s space a r e space c o r r e c t.
Answered by Renu Varma | 05 Apr, 2019, 16:37: PM

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