Home
Class 12
MATHS
The function f(x)=sin(log(x+sqrt(1+x^2))...

The function `f(x)=sin(log(x+sqrt(1+x^2)))` is (a) even function (b) odd function (c) neither even nor odd (d) periodic function

A

even function

B

odd function

C

neither even nor odd

D

periodic function

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=sin(log(x+sqrt(1+x^(2))))`
or `f(-x)=sin[log(-x+sqrt(1+x^(2)))]`
`=sin log((sqrt(1+x^(2))-x)((sqrt(1+x^(2))+x))/((sqrt(1+x^(2))+x)))`
`=sin log[(1)/((x+sqrt(1+x^(2))))]`
`=sin[-log(x+sqrt(1+x^(2)))]`
`= -sin [log(x+sqrt(1+x^(2)))]`
` :. f(-x)= -f(x)`
Therefore, `f(x)` is an odd function.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 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

Q.The function f(x)=ln[x^(3)+sqrt(x^(6)+1)] is an (a) even function (b) odd function (c) increasing function (d) decreasing function

log(x-3) is (A) is an even function (B) an odd function (C) neither even nor odd (D) cannot be determined

Let h(x)=(x)/(5^(x)-1)+(x)/(2)+5 then h(x) is (1) Even Function (2) Odd Fucntion (3) Neither even nor odd (4) Periodic Function

Let f(x)=|x-2|+|x-3|+|x-4| and g(x)=f(x+1). Then 1.g(x) is an even function 2.g(x) is an odd function 3.g(x) is neither even nor odd 4.g(x) is periodic

A function f(x)=(2x(sin x))/(2[(x+21 pi)/(pi)]-41) (1) Even function (3) Neither even nor odd ( 4 ) f(0)=1

Definition, even odd function, Periodic function

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.

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.

Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? (a)G(x) is an odd function (b)G(x)i s an even function (c)G(x) is neither even nor odd function. (d)Whether G(x) is an odd or even function depends on the value of a

If f is an even function and g is an odd function then the function fog is

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. Let f(x)=e^{e^((|x|)sinx})a n dg(x)=e^{e^((|x|)sinx}),x in R , where ...

    Text Solution

    |

  2. The number of solutions of the equation [y+[y]]=2 cosx, where y=(1)...

    Text Solution

    |

  3. The function f(x)=sin(log(x+sqrt(1+x^2))) is (a) even function (b) odd...

    Text Solution

    |

  4. If f(x)=x^m n ,n in N , is an even function, then m is even integer ...

    Text Solution

    |

  5. If f(x)={x^2 sin((pi x)/2), |x|<1; x|x|, |x|>=1 then f(x) is

    Text Solution

    |

  6. If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetrical ...

    Text Solution

    |

  7. If f: Rvec is an invertible function such that f(x)a n df^(-1)(x) are ...

    Text Solution

    |

  8. If f(x)=a x^7+b x^3+c x-5 ,a , b , c are real constants, and f(-7)=7, ...

    Text Solution

    |

  9. If g:[-2,2]vecR , where f(x)=x^3+tanx+[(x^2+1)/P] is an odd function, ...

    Text Solution

    |

  10. Let f:[-1, 10]rightarrowR ,w h e r ef(x)=sinx+[(x^2)/a], be an odd fun...

    Text Solution

    |

  11. f(x)=(cosx)/([(2x)/pi]+1/2), where x is not an integral multiple of pi...

    Text Solution

    |

  12. Let f(x)={(sinx+cosx",",0 lt x lt (pi)/(2)),(a",",x=pi//2),(tan^(2)x+"...

    Text Solution

    |

  13. The period of the function |sin^3(x/2)|+|cos^5(x/5)| is

    Text Solution

    |

  14. If f is periodic, g is polynomial function and f(g(x)) is periodic and...

    Text Solution

    |

  15. The period of function 2^({x}) +sin pi x+3^({x//2})+cos pi x (where {...

    Text Solution

    |

  16. The period of the function f(x)= [6x+7]+cospix-6x , where [dot] denote...

    Text Solution

    |

  17. If f(x) and g(x) are periodic functions with periods 7 and 11, respect...

    Text Solution

    |

  18. The period of the function f(x)=c^((sin^2x) +sin^2 (x+pi/3)+cosxcos(x+...

    Text Solution

    |

  19. Let f(x)={(0.1)^(3[x])}. (where [.] denotes greatest integer function ...

    Text Solution

    |

  20. If the period of (cos(sin(n x)))/(tan(x/n)),n in N ,i s6pi , then n= ...

    Text Solution

    |