Home
Class 12
MATHS
Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y i...

Let `f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+)` such that f(1)=0,f'(1)=2.`
f'(3) is equal to

A

`1/3`

B

`2/3`

C

`1/2`

D

`1/4`

Text Solution

Verified by Experts

The correct Answer is:
b
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|2 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise FUNCTION EXERCISE 5: Matching Type Questions|1 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos
  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)=2. f(x)-f(y) is equal to

Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)=2. f(e) is equal to

If f is a function satisfying f(x+y)= f(x) f(y) for all x,y in N such that f(1)=3 and sum_(x=1)^n f(x)=120 , find the value of n.

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 f: R rarr R be a continuous function given by f(x+y)=f(x)+f(y) for all x,y, in R, if int_0^2 f(x)dx=alpha, then int_-2^2 f(x) dx is equal to

If y=(f_(0)f_(0)f)(x)andf(0)=0,f'(0)=2 then y'(0) is equal to

If 2f(x)=f(x y)+f(x/y) for all positive values of x and y,f(1)=0 and f'(1)=1, then f(e) is.

Let y=f(x) be a differentiable function such that f(−1)=2,f(2)=−1 and f(5)=3 If the equation f (x)=2f(x) has real root. Then find f(x)

Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2 . Prove that 3(int f(x) dx) - x(f(x) + 2) is constant.

ARIHANT MATHS-FUNCTIONS-Exercise (Passage Based Questions)
  1. Consider the equation x+y-[x][y]=0, where [*] is the greatest integer ...

    Text Solution

    |

  2. Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)...

    Text Solution

    |

  3. Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)...

    Text Solution

    |

  4. Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)...

    Text Solution

    |

  5. If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) ...

    Text Solution

    |

  6. If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) ...

    Text Solution

    |

  7. If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) ...

    Text Solution

    |

  8. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3)andf(x)=sqrt(g(x)),f(x) have it...

    Text Solution

    |

  9. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3)andf(x)=sqrt(g(x)),f(x) have it...

    Text Solution

    |

  10. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3) " and " f(x)=sqrt(g(x)), f(x) ...

    Text Solution

    |

  11. Let f :[2,oo)to {1,oo) defined by f (x)=2^(x ^(4)-4x ^(3))and g : [(pi...

    Text Solution

    |

  12. Let f :[2,oo)to {1,oo) defined by f (x)=2^(x ^(4)-4x ^(3))and g : [(pi...

    Text Solution

    |

  13. Let f:[2,infty) rarr [1, infty) defined by f(x)=2^(x^(4)-4x^(2)) and g...

    Text Solution

    |

  14. Let P(x) be a polynomial of degree at most 5 which leaves remainders -...

    Text Solution

    |

  15. Let P(x) be polynominal of degree atmost 5 which leaves remainders -1 ...

    Text Solution

    |

  16. Let P(x) be polynominal of degree atmost 5 which leaves remainders -1 ...

    Text Solution

    |

  17. Consider alpha gt 1 and f:[1/alpha,alpha] rarr [1/alpha,alpha] be bije...

    Text Solution

    |

  18. Consider alpha gt 1 and f:[1/alpha,alpha] rarr [1/alpha,alpha] be bije...

    Text Solution

    |

  19. Consider alpha gt 1 and f:[1/alpha,alpha] rarr [1/alpha,alpha] be bije...

    Text Solution

    |

  20. Let f be real valued function from N to N satisfying. The relation f(m...

    Text Solution

    |