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Asked by sarveshvibrantacademy | 17 May, 2019, 09:44: AM
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G i v e n colon space f comma g space a r e space c o n t i n u o u s space a n d space f comma g colon left square bracket 0 comma 1 right square bracket rightwards arrow R A l s o comma space m a x left curly bracket f left parenthesis x right parenthesis colon x element of left square bracket 0 comma 1 right square bracket right curly bracket equals m a x left curly bracket g left parenthesis x right parenthesis colon x element of left square bracket 0 comma 1 right square bracket right curly bracket rightwards double arrow T h e space g r a p h space o f space b o t h space t h e space f u n c t i o n s space i. e. space f space a n d space g space w i l l space i n t e r s e c t space a t space o n e space p o i n t space a n d space l e t space t h a t space p o i n t space b e space c rightwards double arrow A t space x equals c comma space f left parenthesis c right parenthesis equals g left parenthesis c right parenthesis space f o r space c element of left square bracket 0 comma 1 right square bracket O p t i o n space A left parenthesis f left parenthesis c right parenthesis right parenthesis squared plus 3 f left parenthesis c right parenthesis equals left parenthesis g left parenthesis c right parenthesis right parenthesis squared plus 3 g left parenthesis c right parenthesis left parenthesis f left parenthesis c right parenthesis right parenthesis squared minus left parenthesis g left parenthesis c right parenthesis right parenthesis squared plus 3 f left parenthesis c right parenthesis minus 3 g left parenthesis c right parenthesis equals left parenthesis f left parenthesis c right parenthesis minus g left parenthesis c right parenthesis right parenthesis left parenthesis f left parenthesis c right parenthesis plus g left parenthesis c right parenthesis right parenthesis plus 3 left parenthesis f left parenthesis c right parenthesis minus g left parenthesis c right parenthesis right parenthesis equals open square brackets f left parenthesis c right parenthesis minus g left parenthesis c right parenthesis close square brackets space open square brackets f left parenthesis c right parenthesis plus g left parenthesis c right parenthesis plus 3 close square brackets equals 0 T h u s comma space A space i s space c o r r e c t space O p t i o n space B space i s space n o t space t r u e space a s space left parenthesis f left parenthesis c right parenthesis right parenthesis squared minus left parenthesis g left parenthesis c right parenthesis right parenthesis squared plus f left parenthesis c right parenthesis minus 3 g left parenthesis c right parenthesis not equal to 0 S i m i l a r l y comma space C space i s space n o t space c o r r e c t O p t i o n space D left parenthesis f left parenthesis c right parenthesis right parenthesis squared minus left parenthesis g left parenthesis c right parenthesis right parenthesis squared equals left parenthesis f left parenthesis c right parenthesis minus g left parenthesis c right parenthesis right parenthesis left parenthesis f left parenthesis c right parenthesis plus g left parenthesis c right parenthesis right parenthesis equals 0 T h e r e f o r e comma space D space i s space c o r r e c t. H e n c e comma space o p t i o n space A space a n d space D space a r e space c o r r e c t.
Answered by Renu Varma | 20 May, 2019, 11:51: AM

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