Home
Class 12
MATHS
Let the function f satisfies f(x).f ′ ...

Let the function f satisfies f(x).f ′ (−x)=f(−x).f ′ (x) for all x and f(0)=3 The value of `f(x).f(-x)` for all x is

A

4

B

9

C

12

D

16

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 1|15 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 2|14 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

If f(x)=4x-x^2 for all x in R , then the value of f(a+1)-f(a-1) is:

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be

If for all x,y the function f is defined by f(x)+f(y)+f(x).f(y)=1 and f(x)gt0. Then show f'(x)=0

If f is a real valued differentiable function satisfying | f (x) - f (y) | le (x - y) ^(2) for all real x and y and f (0) =0 then f (1) equals :

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

For x in R , the functions f(x) satisfies 2f(x)+f(1-x)=x^(2) . The value of f(4) is equal to

For x inR - {1} , the function f(x ) satisfies f(x) + 2f(1/(1-x))=x . Find f(2) .

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to

Let the function f:9R to 9R be defined by f(x)=2x+sin for all x in 9R . Then f(x) is

Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for all "x inR. Then, f'(x)f(nx) a. f(x) b. 0 c. f(x)f'(nx) d. none of these

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let the function f satisfies f(x).f ′ (−x)=f(−x).f ′ (x) for all x...

    Text Solution

    |

  2. The total number of distinct x in R for which |{:(x,x^(2),1+x^(3)...

    Text Solution

    |

  3. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

    Text Solution

    |

  4. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

    Text Solution

    |

  5. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  6. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  7. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  8. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

    Text Solution

    |

  9. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

  10. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

  11. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  12. Match the conditions/ expressions in Column I with statement in Column...

    Text Solution

    |

  13. Find x+y+z

    Text Solution

    |

  14. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

    Text Solution

    |

  15. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  16. The value of int(In2)^(In3) (x sinx)dx is

    Text Solution

    |

  17. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

    Text Solution

    |

  18. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(2))dx is (are)

    Text Solution

    |

  19. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^...

    Text Solution

    |

  20. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

    Text Solution

    |

  21. Which of the following is true?

    Text Solution

    |