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Asked by g_archanasharma | 04 Apr, 2019, 08:43: AM
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f space i s space a space f u n c t i o n space d e f i n e d space b y f left parenthesis x right parenthesis equals 1 over x plus 2 to the power of sin to the power of negative 1 end exponent x end exponent plus fraction numerator 1 over denominator square root of x minus 2 end root end fraction I f space x equals 0 rightwards double arrow f left parenthesis x right parenthesis space i s space n o t space d e f i n e d F o r space square root of x minus 2 end root space t o space b e space d e f i n e d comma space w e space s h o u l d space h a v e space x minus 2 greater or equal than 0 space T h u s comma space x greater or equal than 2 N o w comma space sin to the power of negative 1 end exponent x space i s space d e f i n e d space o n l y space f o r space x element of left square bracket negative 1 comma space 1 right square bracket A n d space x not equal to 0 rightwards double arrow x element of left square bracket negative 1 comma space 1 right square bracket space minus open curly brackets 0 close curly brackets space a n d space x greater or equal than 2 space i. e. space x element of left square bracket 2 comma infinity right parenthesis S o comma space t h e r e space i s space n o space i n t e r s e c t i o n space p o i n t space b e t w e e n space t h e space a b o v e space i n t e r v a l s H e n c e comma space n o space x space e x i s t space f o r space w h i c h space f left parenthesis x right parenthesis space i s space d e f i n e d H e n c e comma space t h e space a n s w e r space i s space empty set.
Answered by Renu Varma | 04 Apr, 2019, 10:04: AM

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