Home
Class 12
MATHS
Let f : R to R be a function given by ...

Let ` f : R to R` be a function given by `f(x+y) = f(x) + f(y) ` for all x,y `in`R such that `f(1)= a` Then, `f (x)=`

A

`a^(x)`

B

`ax`

C

`a^(x)`

D

`a+x`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|8 Videos
  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|94 Videos
  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos
  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 Videos
  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|63 Videos

Similar Questions

Explore conceptually related problems

Let f:RtoR be a function given by f(x+y)=f(x)f(y) for all x,y in R .If f'(0)=2 then f(x) is equal to

Let f:R to R be a function given by f(x+y)=f(x)+2y^(2)+"kxy for all "x,y in R If f(1)=2 . Find the value of f(x)

Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){-5}

Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){26}

Let f be a real valued function satisfying f(x+y)=f(x)f(y) for all x, y in R such that f(1)=2 . Then , sum_(k=1)^(n) f(k)=

Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){10 , 37}

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

Let f:R to R be a function given by f(x+y)=f(x) f(y)"for all "x,y in R "If "f(x)=1+xg(x),log_(e)2, "where "lim_(x to 0) g(x)=1. "Then, f'(x)=

LEt F: R->R is a differntiable function f(x+2y) =f(x) + f(2y) +4xy for all x,y in R

Let f:R in R be a function given by f(x+y)=f(x) f(y)"for all"x,y in R "If "f(x) ne 0,"for all "x in R and f'(0)=log 2,"then "f(x)=

OBJECTIVE RD SHARMA ENGLISH-REAL FUNCTIONS -Section I - Solved Mcqs
  1. If f(x) = (x-1)/(x+1), then f(alphax)=

    Text Solution

    |

  2. If f (x) = 27x^(3) -(1)/(x^(3)) and alpha, beta are roots of 3x - (1)/...

    Text Solution

    |

  3. Let f : R to R be a function given by f(x+y) = f(x) + f(y) for all ...

    Text Solution

    |

  4. Let f : R to R be a function given by f(x+y) = f(x) + f(y) for all ...

    Text Solution

    |

  5. Le the be a real valued functions satisfying f(x+1) + f(x-1) = 2 f(x) ...

    Text Solution

    |

  6. If f(x) is a real valued functions satisfying f(x+y) = f(x) +f(y) -yx...

    Text Solution

    |

  7. If f:RtoR satisfies f(x+y)=f(x)+f(y) for all x,y in R and f(1)=7, then...

    Text Solution

    |

  8. If f(x) =ax^(2) + bx + c satisfies the identity f(x+1) -f(x)= 8x+ 3 fo...

    Text Solution

    |

  9. If f(x+y,x -y)= xy then (f(x,y)+f(y,x))/(2)=

    Text Solution

    |

  10. A polynomial function f(x) satisfies the condition f(x)f(1/x)=f(x)+f(1...

    Text Solution

    |

  11. If f: R to R, g , R to R be two funcitons, and h(x) = 2 "min" {f(x) - ...

    Text Solution

    |

  12. If f(x) = cos ([pi]x) +cos [pi x], where [] is the greatest integer fu...

    Text Solution

    |

  13. If f(x)= cos [(pi^(2))/(2)] x + sin[(-pi^(2))/(2)]x,[x] denoting the g...

    Text Solution

    |

  14. If one the roots fo the equation x^(2) +x f(a) + a=0 is the cube of ...

    Text Solution

    |

  15. If the graph of a function f(x) is symmetrical about the line x = a, t...

    Text Solution

    |

  16. If a real function f(x) satisfies the relation f(x) = f(2a -x) for al...

    Text Solution

    |

  17. The largest interval lying in (-(pi)/(2), (pi)/(2)) for which the fun...

    Text Solution

    |

  18. The domain of f (x) = log(2) (2x^(3) - x^(2) - 4x + 2), is

    Text Solution

    |

  19. If f(x) =1- x, x in [-3,3], then the domain of fof (x) is

    Text Solution

    |

  20. If f(x) = sqrt(2-x) and g(x) = sqrt(1-2x), then the domain of fog (x)...

    Text Solution

    |