Home
Class 12
MATHS
Let f be differentiable function satisfy...

Let f be differentiable function satisfying `f((x)/(y))=f(x) - f(y)"for all" x, y gt 0`. If f'(1) = 1, then f(x) is

A

`2g(-1)`

B

0

C

`-2g(1)`

D

`2g(1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|10 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|20 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

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 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

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 differentiable function satisfying the relation f(xy)=xf(y)+yf(x)−2xy .(where x, y >0) and f ′ (1)=3, then find f(x)

Let f(x) be a differentiable bounded function satisfying 2f^(5)(x).f'(x)+2(f'(x))^(3).f^(5)(x)=f''(x) . If f(x) is bounded in between y=k_1 , and y=k_2 , then the number of intergers between k_(1) and k_(2) is/are (where f(0)=f'(0)=0) .

Let f:(0,oo)rarrR be a differentiable function such that f'(x)=2-(f(x))/(x) for all x in (0,oo) and f(1) ne 1. Then

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:R->R be a function satisfying f((x y)/2)=(f(x)*f(y))/2,AAx , y in R and f(1)=f'(1)=!=0. Then, f(x)+f(1-x) is (for all non-zero real values of x ) a.) constant b.) can't be discussed c.) x d.) 1/x

A function y=f(x) satisfies (x+1)f^(')(x)-2(x^(2)+x)f(x) = e^(x^(2))/(x+1), Aax gt -1 . If f(0)=5 , then f(x) is

ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for...

    Text Solution

    |

  2. Area of the region {(x,y) in R^(2):ygesqrt(|x+3|),5ylex+9le15} is eq...

    Text Solution

    |

  3. Let F(x)=int(x)^(x^2+pi/2) 2 cos^(2)dt for all x in R and f:[0,1/2] to...

    Text Solution

    |

  4. The common tangents to the circle x^2=y^2=2 and the parabola y^(2)=8x ...

    Text Solution

    |

  5. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

    Text Solution

    |

  6. In Δ PQR, right-angled at Q, PR + QR = 30 cm and PQ = 10 cm. Determine...

    Text Solution

    |

  7. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)for...

    Text Solution

    |

  8. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

    Text Solution

    |

  9. The area of the region bounded by the curve y=e^x and lines x=0a n dy=...

    Text Solution

    |

  10. The area of the region bounded by the curves y=sqrt[[1+sinx]/cosx] and...

    Text Solution

    |

  11. Find the product of (x - 4)(x - 7)

    Text Solution

    |

  12. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  13. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  14. The area (in sqaure units) of the region {(x,y):x ge 0, x + y le 3, x^...

    Text Solution

    |

  15. The area (in sq. units) of the region {(x,y):y^(2)ge2x and x^(2)+y^(2)...

    Text Solution

    |

  16. The area (in sq units) of the region described by {(x,y):y^(2)le2x and...

    Text Solution

    |

  17. The area (in sq. units) of the quadrilateral formed by the tangents ...

    Text Solution

    |

  18. The area of the region described by A={(x,y):x^(2)+y^(2)le1 and y^(2)l...

    Text Solution

    |

  19. The area bounded by the curves y=sqrt(x),2y+3=x , and x-axis in the 1s...

    Text Solution

    |

  20. The area bounded between the parabolas x^(2)=(y)/(4) and x^(2)=9y and ...

    Text Solution

    |

  21. The area of the region enclosed by the curves y=x, x=e,y=(1)/(x) and t...

    Text Solution

    |