Home
Class 12
MATHS
Suppose f: R->R^+ be a differentiable fu...

Suppose `f: R->R^+` be a differentiable function such that `3f(x+y)=f(x)f(y) AAx ,y in R` with `f(1)=6.` Then the value of `f(2)` is a.`6` b. `9` c. `12` d. `15`

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

Let f(x+y)=f(x)f(y)AA x, in IR, f(6)=5 and f'(0)=1 . Then the value of f' (6) is

If f(x+f(y))=f(x)+yAAx ,y in R a n df(0)=1, then find the value of f(7)dot

Determine the function satisfying f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The value of f(2) is

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The value of f(4) is

A function satisfies the conditions f(x+y)=f(x) + f(y), AA x, y in R then f is

Let f be a function such that f(x + y) = f(x) + f(y) forall x , y in R , if f(1) = k, then show that f(n) is equal to nk.

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

f is a function such that f(x + y) = f(x) .f(y), forall x, y in R , if f(1) = 3, then find sum_(r = 1)^n f(r) .

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in R . If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let y=x^(3)-8x+7 and x=f(t)." If "(dy)/(dt)=2 and x=3 at t = 0," then ...

    Text Solution

    |

  2. f is a strictly monotonic differentiable function with f^(prime)(x)=1/...

    Text Solution

    |

  3. Suppose f: R->R^+ be a differentiable function such that 3f(x+y)=f(x)f...

    Text Solution

    |

  4. Vertices of a variable acute angled triangle A B C lies on a fixed cir...

    Text Solution

    |

  5. In a question a student was given to find the derivative of the prod...

    Text Solution

    |

  6. A nonzero polynomial with real coefficient has the property that f(x)=...

    Text Solution

    |

  7. If 'f' is an increasing function from RtoR such that f^(prime)prime(x)...

    Text Solution

    |

  8. If x=(1+t)/(t^(3)),y=(3)/(2t^(2))+(2)/(t) then x((dy)/(dx))^(3)-(dy)/(...

    Text Solution

    |

  9. Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly...

    Text Solution

    |

  10. If f(x)={sin((a-x)/2)t a n[(pix)/(2a)] for x > a and ([cos((pix)/(2a...

    Text Solution

    |

  11. Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):}. If f...

    Text Solution

    |

  12. Statement 1: Minimum number of points of discontinuity of the functi...

    Text Solution

    |

  13. Let f(x)=[tanx[cotx]], x in [(pi)/(12),(pi)/(2)), (where [.] denotes t...

    Text Solution

    |

  14. Let f[-2,2]rarrR be a continuous function such that f(x)assumes only i...

    Text Solution

    |

  15. If f(x)=prod(n=1)^(100)(x-n)^(n(101-n)); then (f(101))/(f'(101))=

    Text Solution

    |

  16. A curve in the xy-plane is parametrically given by x=t+t^3a n dy=t^2,w...

    Text Solution

    |

  17. Number of points of discontinuity of f(x)=[sin^(-1)x]-[x] in its domai...

    Text Solution

    |

  18. If g(x)=(lim)(mtooo)(x^mf(x)+h(x)+3)/(2x^m+4x+1) when x!=1a n dg(1)=e^...

    Text Solution

    |

  19. Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable...

    Text Solution

    |

  20. If f(x)=|[(x-a)^4, (x-a)^3, 1] , [(x-b)^4, (x-b)^3,1] , [(x-c)^4, (x-c...

    Text Solution

    |