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Range of cos inverse ((x^2 + x + 1)/(x^4 + 1)) . Please provide a detailed solution
Asked by kunalgaurav39 | 27 Apr, 2019, 12:09: PM
answered-by-expert Expert Answer
L e t space f left parenthesis x right parenthesis equals cos to the power of negative 1 end exponent open parentheses fraction numerator x squared plus x plus 1 over denominator x to the power of 4 plus 1 end fraction close parentheses T o space f i n d space t h e space r a n g e space o f space f W e space k n o w space t h a t comma space x to the power of 4 greater or equal than 0 space a l w a y s rightwards double arrow x to the power of 4 plus 1 greater or equal than 0 space a l w a y s A l s o comma space x squared greater or equal than x space rightwards double arrow space x squared plus x plus 1 greater or equal than 0 space a l w a y s rightwards double arrow fraction numerator x squared plus x plus 1 over denominator x to the power of 4 plus 1 end fraction greater or equal than 0 space a l w a y s i. e. space fraction numerator x squared plus x plus 1 over denominator x to the power of 4 plus 1 end fraction element of left square bracket 0 comma infinity right parenthesis A l s o comma space f o r space cos to the power of negative 1 end exponent open parentheses fraction numerator x squared plus x plus 1 over denominator x to the power of 4 plus 1 end fraction close parentheses space t o space b e space d e f i n e d space i t space m u s t space s a t i s f y space t h a t space fraction numerator x squared plus x plus 1 over denominator x to the power of 4 plus 1 end fraction element of left square bracket negative 1 comma 1 right square bracket N o w comma space left square bracket negative 1 comma 1 right square bracket intersection left square bracket 0 comma infinity right square bracket equals left square bracket 0 comma 1 right square bracket T h u s comma space cos to the power of negative 1 end exponent open parentheses fraction numerator x squared plus x plus 1 over denominator x to the power of 4 plus 1 end fraction close parentheses element of open square brackets 0 comma straight pi over 2 close square brackets H e n c e comma space t h e space r a n g e space o f space f left parenthesis x right parenthesis space i s space open square brackets 0 comma straight pi over 2 close square brackets
Answered by Renu Varma | 29 Apr, 2019, 13:17: PM

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