Home
Class 12
MATHS
A function f : R -> R^+ satisfies f(x+y)...

A function `f : R -> R^+` satisfies `f(x+y)= f(x) f(y) AA x in R` If `f'(0)=2` then `f'(x)=`

A

`f(x)`

B

`2f(x)`

C

`(1)/(f(x))`

D

`(2)/(f(x))`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TIPS

    FIITJEE|Exercise OBJECTIVE|84 Videos
  • TIPS

    FIITJEE|Exercise ASSERTION REASONING|8 Videos
  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos
  • TEST PAPERS

    FIITJEE|Exercise MATHEMATICS|328 Videos
  • TRIGNOMETRIC RATIOS AND IDENTITIES

    FIITJEE|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

A function f:R rarr R^(+) satisfies f(x+y)=f(x)f(y)AA x in R If f'(0)=2 then f'(x)=

A function f : R to R satisfies the equation f(x+y) = f (x) f(y), AA x, y in R and f (x) ne 0 for any x in R . Let the function be differentiable at x = 0 and f'(0) = 2. Show that f'(x) = 2 f(x), AA x in R. Hence, determine f(x)

Let f(x) be a continuous & differentiable function on R satisfying f(-x)=f(x)&f(3+x)=f(3-x)AA x in R . If f'(1)=-5 then f'(7) =

Let f(x+y)+f(x-y)=2f(x)f(y)AA x,y in R and f(0)=k, then

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b

A function f : R rarr R satisfies the equation f(x+y) = f(x). f(y) for all x y in R, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2 , then prove that f' = 2f(x) .

Let f:R rarr R be a differential function satisfy f(x)=f(x-y)f(y)AA x,y in R and f'(0)=a,f'(2)=b then f'(-2)=

If f:R rarr R satisfies,f(x+y)=f(x)+f(y),AA x,y in R and f(1)=4,thensum_(r=1)^(n)f(r)

Let f:R rarr R 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

FIITJEE-TIPS-ASSIGNMENT (SECTION (I): MCQ (SINGLE CORRECT)
  1. If f(x)=ax when a<1 and f(x)= ax^2+bx+2 when a >= 1 then the values of...

    Text Solution

    |

  2. The function f(x) = tan ^-1 x - In(1 + x^2) is increasing for

    Text Solution

    |

  3. A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)...

    Text Solution

    |

  4. If f(x) = x^3 + 3x^2 + 12x-2sin x, where f : R ->R, then

    Text Solution

    |

  5. y = f(x) be a real valued function with domain as all real numbers. If...

    Text Solution

    |

  6. if f(x)=sqrt(sec^-1((2-|x|)/4)) then the domain of f(x) is

    Text Solution

    |

  7. If f(x) ={x} + sin ax (where { } denotes the fractional part function)...

    Text Solution

    |

  8. Which of the following is differentiable in the interval (1, 2)?

    Text Solution

    |

  9. If f(x)=lim(n-&gt;oo)[2x+4x^3+6x^5++2n x^(2n-1)] (0ltxlt1) then int f(...

    Text Solution

    |

  10. The integer n for which the lim(x to 0)(cos^(2)x-cosx-e^(x)cosx+e^(x...

    Text Solution

    |

  11. If f(x)=(tan(pi/4+(log)e x))^((log)x e) is to be made continuous at x=...

    Text Solution

    |

  12. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

    Text Solution

    |

  13. If f is twice differentiable such that f"(x)=-f(x) f'(x)=g(x),h'(x)=...

    Text Solution

    |

  14. lim(x->0) (tan^2[x])/([x]^2), where [] represents greatest integer fun...

    Text Solution

    |

  15. lim(xrarr1^(+))(log(sqrt2)sqrt2x)^(1/({x})) where [ ] represents great...

    Text Solution

    |

  16. The value of lim(xto(pi)/4)(4sqrt(2)-(cosx+sinx)^(5))/(1-sin2x) is

    Text Solution

    |

  17. lim(xrarrpi)([sinx]+x) is

    Text Solution

    |

  18. The slope of the tangent of the curve y=int0^x (dx)/(1+x^3) at the poi...

    Text Solution

    |

  19. The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the...

    Text Solution

    |

  20. The difference between the greatest and the least values of the functi...

    Text Solution

    |