Home
Class 12
MATHS
If f(x)={xcosx+(log)e((1-x)/(1+x))a; x=...

If `f(x)={xcosx+(log)_e((1-x)/(1+x))a; x=0; x!=0` is odd, then `a_______,`

Text Solution

Verified by Experts

The correct Answer is:
0
For `x ne 0, f(x)=x cosx + log_(e)((1-x)/(1+x))`
` :. f(-x)=(-x)cos(-x)+log_(e)((1+x)/(1-x))`
`= -x cosx-log_(e)((1-x)/(1+x))`
`= -f(x)`
For `x=0`, we must have `f(-x)= -f(x)`
` :. a= -a`
` :. a=0`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise JEE Previous Year|12 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Solved Examples And Exercises|498 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Matrix)|9 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

f(x)={(log(1+2ax)-log(1-bx))/(x),x!=0x=0

Let f(x)=(e^(x)x cos x-x log_(e)(1+x)-x)/(x^(2)),x!=0 If f(x) is continuous at x=0, then f(0) is equal to

If f(x)=(e^(2x)-(1+4x)^(1/2))/(ln(1-x^(2))) for x!=0, then f has

If f(x)= {{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

If f(x) f(x) = (log{(1+x)^(1+x)}-x)/(x^(2)), x != 0 , is continuous at x = 0 , then : f(0) =

If f(x)={(e^((1)/(x))/(1+e^((1)/(x)))",", x ne0),(0",",x=0):} , then

If f(x) = (log_(e)(1+x^(2)tanx))/(sinx^(3)), x != 0 is continuous at x = 0 then f(0) must be defined as

'f(x)={(e^(^^)x-1)/(log(1+2x)),|x!=0Kx=0at

If f(x) is continuous at x=0 , where f(x)=(log(1+x+x^(2))+log(1-x+x^(2)))/(sin x) , for x!=0 , then f(0)=

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Numerical)
  1. The number of points on the real line where the function f(x)-log- Ix-...

    Text Solution

    |

  2. The number of integral values of x for which ((pi/(2^tan^((-1)x-4)))(x...

    Text Solution

    |

  3. If f(x)={xcosx+(log)e((1-x)/(1+x))a; x=0; x!=0 is odd, then a,

    Text Solution

    |

  4. The number of integers in the range of the function f(x)=|4((sqrt(c...

    Text Solution

    |

  5. The number of integers in the domain of function, satisfying f(x)+f(x^...

    Text Solution

    |

  6. If a polynomial function f(x) satisfies f(f(f(x))=8x+21 , where pa n d...

    Text Solution

    |

  7. If f(x) is an odd function, f(1)=3,f(x+2)=f(x)+f(2), then the value of...

    Text Solution

    |

  8. Let f: RvecR be a continuous onto function satisfying f(x)+f(-x)=0AAx ...

    Text Solution

    |

  9. The set of all real values of x for which the funciton f(x) = sqrt(sin...

    Text Solution

    |

  10. Suppose that f is an even, periodic function with period 2,a n dt h a ...

    Text Solution

    |

  11. If f(x)=sqrt(4-x^2)+sqrt(x^2-1) , then the maximum value of (f(x))^2 i...

    Text Solution

    |

  12. The function f(x)=(x+1)/(x^3+1) can be written as the sum of an even f...

    Text Solution

    |

  13. If T is the period of the function f(x)=[8x+7]+|tan2pix+cot2pix|-8x] (...

    Text Solution

    |

  14. An even polynomial function f(x) satisfies a relation f(2x)(1-f(1/(2x)...

    Text Solution

    |

  15. If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4=1, then (gof)(x...

    Text Solution

    |

  16. Let E={1,2,3,4,} and F={1,2}. Then the number of onto functions from E...

    Text Solution

    |

  17. The function of f is continuous and has the property f(f(x))=1-xdot Th...

    Text Solution

    |

  18. A function f from integers to integers is defined as f(n)={(n+3",",...

    Text Solution

    |

  19. If theta is the fundamental period of the function f(x) = sin^99 x+si...

    Text Solution

    |

  20. If x=4/9 satisfies the equation (log)a(x^2-x+2)>(log)a(-x^2+2x+3), the...

    Text Solution

    |