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Asked by g_archanasharma | 19 Mar, 2019, 22:03: PM
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G i v e n colon space f left parenthesis x right parenthesis equals m i n left curly bracket x minus left square bracket x right square bracket comma negative x minus left square bracket negative x right square bracket right curly bracket comma space g left parenthesis x right parenthesis equals vertical line 2 minus vertical line x minus 2 vertical line vertical line space a n d space h left parenthesis x right parenthesis equals fraction numerator vertical line sin space x vertical line over denominator sin space x end fraction space w h e r e space x element of left square bracket negative 2 comma 2 right square bracket space a n d space x not equal to 0 space f o r space h left parenthesis x right parenthesis N o w comma space i f space x space i s space a n space i n t e g e r rightwards double arrow space f left parenthesis x right parenthesis equals m i n left curly bracket x minus x comma negative x minus left parenthesis negative x right parenthesis right curly bracket equals m i n left curly bracket 0 comma 0 right curly bracket equals 0 space......... space left parenthesis i right parenthesis I f space x space i s space n o t space a n space i n t e g e r comma space t h e n space left square bracket x right square bracket equals x minus left curly bracket x right curly bracket comma space w h e r e space left curly bracket x right curly bracket space d e n o t e s space f r a c t i o n a l space p a r t space o f space x rightwards double arrow f left parenthesis x right parenthesis equals m i n left curly bracket x minus left parenthesis x minus left curly bracket x right curly bracket right parenthesis comma space minus x minus left parenthesis negative x minus left curly bracket negative x right curly bracket right parenthesis right curly bracket rightwards double arrow f left parenthesis x right parenthesis equals m i n left curly bracket left curly bracket x right curly bracket comma space left curly bracket negative x right curly bracket right curly bracket space........ space left parenthesis i i right parenthesis F r o m space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis comma space w e space h a v e f left parenthesis x right parenthesis equals m i n left curly bracket 0 comma space left curly bracket x right curly bracket comma space left curly bracket negative x right curly bracket right curly bracket W e space k n o w space t h a t space f r a c t i o n a l space p a r t space o f space x space a n d space i x space w i l l space b e space t h e space s a m e rightwards double arrow f left parenthesis x right parenthesis equals m i n left curly bracket 0 comma space left curly bracket x right curly bracket right curly bracket A l s o comma space f r a c t i o n a l space p a r t space i s space b e t w e e n space 0 space a n d space 1 rightwards double arrow left curly bracket x right curly bracket element of left parenthesis 0 comma 1 right parenthesis rightwards double arrow f left parenthesis x right parenthesis equals 0 N o w comma space c o n s i d e r space t h e space e q u a t i o n x squared plus left square bracket f left parenthesis x right parenthesis right square bracket squared equals 1 comma space w h e r e space minus 1 less or equal than x less or equal than 1 rightwards double arrow x squared plus 0 equals 1 rightwards double arrow x squared equals 1 rightwards double arrow x equals plus-or-minus 1 T h u s comma space x space c a n space t a k e space o n l y space t w o space v a l u e s. H e n c e comma space t h e space n u m b e r space o f space s o l u t i o n s space i s space 2.
Answered by Renu Varma | 20 Mar, 2019, 15:46: PM

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