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Amrita Ishat Bhardwaj
Asked: 2022-11-04T19:04:08+05:30 In:

Statement-1: Every function can be uniquely expressed as the sum of an even function and an odd function.
Statement-2: The set of values of parameter a for which the functions f(x) defined as ` f(x)=tan(sinx)+[(x^(2))/(a)]` on the set [-3,3] is an odd function is , `[9,oo)`
A. Statement-1 is True, Statement-2 is True, statement-2 is a correct explanation for the statement-1 .
B. Statement-1 is True, Statement-2 is True, statement-2 is not a correct explanation for the statement-1 .
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False , Statement-2 is True.

Statement-1: Every function can be uniquely expressed as the sum of an even function and an odd function.
Statement-2: The set of values of parameter a for which the functions f(x) defined as ` f(x)=tan(sinx)+[(x^(2))/(a)]` on the set [-3,3] is an odd function is , `[9,oo)`
A. Statement-1 is True, Statement-2 is True, statement-2 is a correct explanation for the statement-1 .
B. Statement-1 is True, Statement-2 is True, statement-2 is not a correct explanation for the statement-1 .
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False , Statement-2 is True.
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1 Answer

  1. Correct Answer – B
    Clearly , statement-1 is true .(see theory )
    It is given that `f(x)=tan(sinx)+[(x^(2))/(a)]` is an odd function.
    `:.f(-x)=-f(x)`
    `implies -tan (sinx)+[(x^(2))/(a)]=-tan(sinx)-[(x^(2))/(a)]`
    `implies 2[(x^(2))/(a)=0`
    `implies 0le (x^(2))/(a) lt 1`
    `implies a gt 0 and 0 lex^(2) lt a ” for all ” x in[-3,3]`
    `implies a gt 9, i.e., a in [9,oo)`
    so, statement-2 is also true.

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