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Let f:(-pi/2,pi/2)vecR be given by f(x)=...

Let `f:(-pi/2,pi/2)vecR` be given by `f(x)=(log(sec"x"+tan"x"))^3` then `f(x)` is an odd function `f(x)` is a one-one function `f(x)` is an onto function `f(x)` is an even function

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f(x)=(log(sec x+tan x)^(3) then f(x) is one one,onto,even or odd

Statement 1: If f(x) is an odd function,then f'(x) is an even function.Statement 2: If f'(x) is an even function,then f(x) is an odd function.

Knowledge Check

  • Statement-1: The function f(x) given by f(x)=sin^(-1){log(x+sqrt(x^(2)+1))} is an odd function. Statement:2 The composition of two odd functions is an odd function.

    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 I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and g(x)=f'(x) is an even function , then f(x) is an odd function.

    A
    Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement 1.
    B
    Statement I is true, Statement II is also true , Statement II is not the correct explanation of Statement II.
    C
    Statement I is true, Statement II is false
    D
    Statement I is false , Statement II is true

  • Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

    A
    constant
    B
    logarithmic
    C
    exponential
    D
    linear

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