Home
Class 12
MATHS
If f(x+y)=f(x)+f(y) for all real x and y...

If `f(x+y)=f(x)+f(y)` for all real x and y, show that `f(x)=xf(1)`.

Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise TRIGONOMETRY|148 Videos
  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise ALGEBRA|141 Videos
  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos
  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

If f(x+y) = f(x) * f(y) for all real x and y and f(5)=2,f'(0) = 3 , find f'(5).

If f(x + y) = f(x) - f(y), forall x, y in R , then show that f(3) = f(1)

Let f((x+y)/(2))=1/2 |f(x) +f(y)| for all real x and y, if f '(0) exists and equal to (-1), and f(0)=1 then f(2) is equal to-

If f(x+y)=f(x). f(y) for all x and y and f(5)=2, f'(0)=4, then f '(5) will be

If f(xy)=(f(x))/y+(f(y))/x holds for all real x and y greater than 0 and f(x) is a differentiable function for all x >0 such that f(e)=1/e , then find f(x)

Let f(x+y)=f(x)+f(y)+2x y-1 for all real x and y and f(x) be a differentiable function. If f^(prime)(0)=cosalpha, the prove that f(x)>0AAx in Rdot

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)^nf(x)=120 , find the value of n.

Let f(x+y)=f(x)+f(y) for all real x and y . If f (x) is continuous at x = 0 , show it is continuous for all real values of x .

If f(x + y) = f(x)f(y) for all x, y and and f(x) = 1 + x g(x), where lim_(xrarr0)g(x)=1 ) , show that f'(x) = f(x).

If f(x+y)=f(x)dotf(y) for all real x , ya n df(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^2) is an even function.

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-WBJEE 2026
  1. If f(x+y)=f(x)+f(y) for all real x and y, show that f(x)=xf(1).

    Text Solution

    |

  2. 7^(2n)+16n-1(n""inNN) is divisble by

    Text Solution

    |

  3. The number of irrational terms in the expansion of (3^((1)/(6))+5^((1)...

    Text Solution

    |

  4. Let P and T be the subsets of X-Y plane defined by p={(x,y):xgt0,ygt...

    Text Solution

    |

  5. If e^(sinx)-e^(-sinx)-4=0, then the number of real values of x is

    Text Solution

    |

  6. The angles of a triangle are in the ratio 2:3:7 and the raidus of the ...

    Text Solution

    |

  7. A variable line passes through a fixed point (x(1),y(1)) and meets the...

    Text Solution

    |

  8. A straight line through the point (3, -2) is inclined at an angle 60^(...

    Text Solution

    |

  9. A variable line passes through the fixed point (alpha,beta). The locus...

    Text Solution

    |

  10. If the point of intersection of the lines 2ax+4ay+c=0 and 7bx+3by-d=0 ...

    Text Solution

    |

  11. A variable circle passes through the fixed point A(p,q) and touches x-...

    Text Solution

    |

  12. If P(0,0,)Q(1,0)andR((1)/(2),(sqrt3)/(2)) are three given points, then...

    Text Solution

    |

  13. For the hyperbola (x^(2))/(cos^(2)alpha)-(y^(2))/(sin^(2)alpha)=1, whi...

    Text Solution

    |

  14. S and T are the foci of an ellipse and B is the end point of the minor...

    Text Solution

    |

  15. The equation of the directrices of the hyperbola 3x^(2)-3y^(2)-18x+12y...

    Text Solution

    |

  16. P is the extremity of the latusrectum of ellipse 3x^(2)+4y^(2)=48 in t...

    Text Solution

    |

  17. For any non-zero complex number z, the minimum value of |z|+|z-1| is

    Text Solution

    |

  18. The polar coordinate of point P is (2,(pi)/(4)). The polar coordinate ...

    Text Solution

    |

  19. The length of conjugate axis of a hyperbola is greater than the length...

    Text Solution

    |

  20. The value of lim(xto0+)(x)/(p)[(q)/(x)] is

    Text Solution

    |

  21. Let x(1),x(2) be the roots of x^(2)-3x+a=0andx(3),x(4) be the roots of...

    Text Solution

    |