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Asked by vishakhachandan026 | 13 May, 2019, 11:56: AM
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f left parenthesis x right parenthesis equals log subscript 2 left parenthesis 2 minus log subscript square root of 2 end subscript left parenthesis 16 sin squared x plus 1 right parenthesis right parenthesis equals log subscript 2 left parenthesis 2 left parenthesis log subscript square root of 2 end subscript square root of 2 right parenthesis minus log subscript square root of 2 end subscript left parenthesis 16 sin squared x plus 1 right parenthesis right parenthesis equals log subscript 2 left parenthesis log subscript square root of 2 end subscript space 2 minus log subscript square root of 2 end subscript left parenthesis 16 sin squared x plus 1 right parenthesis right parenthesis equals log subscript 2 open parentheses log subscript square root of 2 end subscript open parentheses fraction numerator 2 over denominator 16 sin squared x plus 1 end fraction close parentheses close parentheses W e space k n o w space t h a t comma space minus 1 less or equal than sin space x less or equal than 1 rightwards double arrow 0 less or equal than sin squared x less or equal than 1 rightwards double arrow 1 less or equal than 16 sin squared x plus 1 less or equal than 17 rightwards double arrow 1 over 17 less or equal than fraction numerator 1 over denominator 16 sin squared x plus 1 end fraction less or equal than 1 rightwards double arrow 2 over 17 less or equal than fraction numerator 2 over denominator 16 sin squared x plus 1 end fraction less or equal than 2 T h e r e f o r e comma space m a x space v a l u e space o f space fraction numerator 2 over denominator 16 sin squared x plus 1 end fraction space i s space 2 S o comma space m a x space v a l u e space o f space f left parenthesis x right parenthesis space i s f left parenthesis x right parenthesis subscript m a x end subscript equals log subscript 2 open parentheses log subscript square root of 2 end subscript open parentheses 2 close parentheses close parentheses equals log subscript 2 open parentheses 2 close parentheses equals 1 T o space f i n d space t h e space m i n i m u m space r a n g e colon W e space k n o w space t h a t comma space log space f u n c t i o n space i s space d e f i n e d space f o r space p o s i t i v e space v a l u e s rightwards double arrow 2 minus log subscript square root of 2 end subscript left parenthesis 16 sin squared x plus 1 right parenthesis greater than 0 rightwards double arrow 2 greater than log subscript square root of 2 end subscript left parenthesis 16 sin squared x plus 1 right parenthesis rightwards double arrow 2 greater than 16 sin squared x plus 1 S o comma space w e space g e t space t h e space m a x space v a l u e space o f space 16 sin squared x plus 1 space i s space 2 W h e n space 16 sin squared x plus 1 space i s space m a x comma space f left parenthesis x right parenthesis space i s space m i n i m u m log subscript square root of 2 end subscript left parenthesis 16 sin squared x plus 1 right parenthesis equals log subscript square root of 2 end subscript space 2 equals 2 rightwards double arrow 2 minus log subscript square root of 2 end subscript left parenthesis 16 sin squared x plus 1 right parenthesis equals 0 S o space w e space c a n space s a y space 2 minus log subscript square root of 2 end subscript left parenthesis 16 sin squared x plus 1 right parenthesis space i s space a l w a y s space g r e a t e r space t h a n space 0 space a n d space log subscript 2 space 0 to the power of plus space a p p r o a c h e s space minus infinity T h e r e f o r e comma space f left parenthesis x right parenthesis subscript m i n end subscript equals negative infinity H e n c e comma space r a n g e space o f space f left parenthesis x right parenthesis space i s space left parenthesis negative infinity comma 1 right square bracket
Answered by Renu Varma | 13 May, 2019, 12:31: PM

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