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Asked by g_archanasharma | 04 Feb, 2019, 05:32: AM
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A space f u n c t i o n space f left parenthesis x right parenthesis space i s space s a i d space t o space b e space e v e n space i f space f left parenthesis negative x right parenthesis equals f left parenthesis x right parenthesis space a n d space i t space i s space o d d space i f space f left parenthesis negative x right parenthesis equals negative f left parenthesis x right parenthesis left parenthesis 1 right parenthesis f left parenthesis x right parenthesis equals log subscript 10 open parentheses x cubed plus square root of x to the power of 6 plus 1 end root close parentheses f left parenthesis negative x right parenthesis equals log subscript 10 open parentheses left parenthesis negative x right parenthesis cubed plus square root of left parenthesis negative x right parenthesis to the power of 6 plus 1 end root close parentheses space space space space space space space space space space equals log subscript 10 open parentheses negative x cubed plus square root of x to the power of 6 plus 1 end root close parentheses not equal to negative f left parenthesis x right parenthesis not equal to f left parenthesis x right parenthesis T h e r e f o r e comma space f space i s space n e i t h e r space e v e n space n o r space o d d. left parenthesis 2 right parenthesis f left parenthesis x right parenthesis equals x to the power of 4 space open parentheses fraction numerator a to the power of x plus 1 over denominator a to the power of x minus 1 end fraction close parentheses f left parenthesis negative x right parenthesis equals left parenthesis negative x right parenthesis to the power of 4 space open parentheses fraction numerator a to the power of negative x end exponent plus 1 over denominator a to the power of negative x end exponent minus 1 end fraction close parentheses space space space space space space space space space equals x to the power of 4 space open parentheses fraction numerator a to the power of x plus 1 over denominator 1 minus a to the power of x end fraction close parentheses space space space space space space space space space equals negative x to the power of 4 space open parentheses fraction numerator a to the power of x plus 1 over denominator a to the power of x minus 1 end fraction close parentheses space space space space space space space space space equals negative f left parenthesis x right parenthesis T h u s comma space f space i s space o d d. left parenthesis 3 right parenthesis f left parenthesis x right parenthesis equals x vertical line x vertical line f left parenthesis negative x right parenthesis equals left parenthesis negative x right parenthesis vertical line minus x vertical line space space space space space space space space space space equals negative x vertical line x vertical line space space space space space space space space space space equals negative f left parenthesis x right parenthesis T h u s comma space f space i s space o d d. left parenthesis 4 right parenthesis f left parenthesis x right parenthesis equals cos open curly brackets log subscript 10 open parentheses fraction numerator x plus 100 over denominator x minus 100 end fraction close parentheses close curly brackets f left parenthesis negative x right parenthesis equals cos open curly brackets log subscript 10 open parentheses fraction numerator left parenthesis negative x right parenthesis plus 100 over denominator left parenthesis negative x right parenthesis minus 100 end fraction close parentheses close curly brackets space space space space space space space space space equals cos open curly brackets log subscript 10 open parentheses fraction numerator negative x plus 100 over denominator negative x minus 100 end fraction close parentheses close curly brackets space space space space space space space space space equals cos open curly brackets log subscript 10 open parentheses fraction numerator negative left parenthesis x minus 100 right parenthesis over denominator negative left parenthesis x plus 100 right parenthesis end fraction close parentheses close curly brackets space space space space space space space space space equals cos open curly brackets log subscript 10 open parentheses fraction numerator x minus 100 over denominator x plus 100 end fraction close parentheses close curly brackets space space space space space space space space space equals cos open curly brackets log subscript 10 open parentheses fraction numerator x plus 100 over denominator x minus 100 end fraction close parentheses to the power of left parenthesis negative 1 right parenthesis end exponent close curly brackets space space space space space space space space space equals cos open curly brackets negative space log subscript 10 open parentheses fraction numerator x plus 100 over denominator x minus 100 end fraction close parentheses close curly brackets space space space space space space space space space equals cos open curly brackets log subscript 10 open parentheses fraction numerator x plus 100 over denominator x minus 100 end fraction close parentheses close curly brackets space............... space S i n c e space cos open parentheses negative x close parentheses equals cos space x space space space space space space space space space equals f left parenthesis x right parenthesis T h e r e f o r e comma space f left parenthesis negative x right parenthesis equals f left parenthesis x right parenthesis H e n c e comma space f space i s space e v e n.
Answered by Renu Varma | 04 Feb, 2019, 11:32: AM

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