Home
Class 12
MATHS
If 2f(x)=f(x y)+f(x/y) for all positive ...

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.

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

  • TIPS

    FIITJEE|Exercise PARAGRAPH BASED (MULTIPLE CHOICE) (COMPREHENSION - I)|39 Videos

  • TEST PAPERS

    FIITJEE|Exercise MATHEMATICS|328 Videos

  • TRIGNOMETRIC RATIOS AND IDENTITIES

    FIITJEE|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

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

If f((x)/(y))=(f(x))/(f(y)) for all x,y in R,y!=0 and f(t)!=0, if t!=0 and f'(1)=3 then f(x) is

if f(x+y)=f(x)+f(y)+c, for all real x and y and f(x) is continuous at x=0 and f'(0)=-1 then f(x) equals to

f(x/y)=f(x)/f(y) and f'(1)=2024 , then

f(x+(1)/(y))+f(x-(1)/(y))=2f(x)*f((1)/(y)) for all xy in R-{0} and f(0)=(1)/(2), then f(4) is

If f (x+y) =f (x) f(y) for all x,y and f (0) ne 0, and F (x) =(f(x))/(1+(f (x))^(2)) then:

If f(x)=(x)/(x-1)=(1)/(y) then the value of f(y)

If f is a differentiable function satisfying 2f(x)=f(xy)+f((x)/(y)),AA x,y in R^(+), f(1)=0 and f'(1)=(1)/(ln6), then f(7776) =

FIITJEE-TIPS-NUMERICAL BASED QUESTIONS
  1. If alpha is a the absolute maximum value of the expression (3x^(2)+2x-...

    Text Solution

    |

  2. The value of (8sqrt2)/(pi)int(0)^(1)((1-x^(2))/(1+x^(2)))(dx)/(sqrt(1+...

    Text Solution

    |

  3. The value of lim(xrarr0)(16-16 cos (1-cos x))/(x^(4)) is

    Text Solution

    |

  4. The value of lim(xrarrpi//2)12 tan^(2)x[sqrt(6+3 sin x-2cos^(2)x)-sqrt...

    Text Solution

    |

  5. f(x)=sqrt(x-1)+sqrt(2-x)andg(x)=x^(2)+bx+c are two given functions suc...

    Text Solution

    |

  6. If f(x+y+z)=f(x)+f(y)+f(z) with f(1)=1 and f(2)=2 and x,y, z epsilonR ...

    Text Solution

    |

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

    Text Solution

    |

  8. The value of f(0) so that the function f(x)=(1)/(x)-(1)/(sinx) is cont...

    Text Solution

    |

  9. Let f be a positive function. If I1 = int(1-k)^k x f[x(1-x)]\ dx and I...

    Text Solution

    |

  10. Find the area enclosed by the curves max(|x+y|,|x-y|)=1

    Text Solution

    |

  11. The number of points at which the function, f (x)={{:(min {|x|"," x ...

    Text Solution

    |

  12. f(x)=[x] and g(x)={{:(1",",x gt1),(2",", x le 1):}, (where [.] represe...

    Text Solution

    |

  13. underset(xto1)lim[cosec(pix)/(2)]^(1//(1-x)) (where [.] represents the...

    Text Solution

    |

  14. int(1)^(7)(log sqrt(x))/(log sqrt(8-x)+log sqrt(x))dx=

    Text Solution

    |

  15. Period of function 2^({x})+sin 2pix+3^({x//2)}+cos 2pix, (where {x} de...

    Text Solution

    |

  16. Let y=(a sin x+(b+c)cosx)e^(x+d) where a, b, c, d are parameters. The ...

    Text Solution

    |

  17. lim(n->oo)(n^(alpha)sin^2n !)/(n+1), 0ltalphalt1, is equal to :

    Text Solution

    |

  18. If f(x) ge 0 for all x in [0,10] and int(2)^(8) f(x)=0, then f(7) is

    Text Solution

    |

  19. The area of quadrilateral combined equation of whose sides are (x^(2...

    Text Solution

    |

  20. The number of points of non differentiability of y=|log|x|| are

    Text Solution

    |