Home
Class 12
MATHS
If f(x+y)=2f(x) f(y) for all x,y where f...

If `f(x+y)=2f(x) f(y)` for all x,y where f'(0)=3 and f'(4)=2, then f'(4) is equal to

Text Solution

Verified by Experts

The correct Answer is:
4
`f(4)=limg_(hrarr0)(f(4+h)-f(4))/h`
`=limg_(hrarr)(f(4+h)-f(4+0))/h`
`= lim_(hrarr0)(2f(4)f(4)-2f(4)f(0))/h` (using `f(x+y)=2f(x)f(y))`
`=2f(4).lim_(hrarr0)(f(h)-f(0))/h=2f(4)f(0)=2xx2xx1=4`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

"Let" f(x+y)=f(x)f(y) "for all x,y, where" f(0)ne0 . If f'(0)=2, then f(x) is equal to

If 2f(x+y)=f(x).f(y) for all real x, y. where f'(0)=3 and f(4)=25 , then the value of f'(4) is equal to

Let f(x+y)=f(x)*f(y) for all x y where f(0)!=0 .If f(5)=2 and f'(0)=3 then f'(5) is equal to

If f(x+y)=f(x)f(y) for all real x and y, f(6)=3 and f'(0)=10 , then f'(6) is

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

f(x+y)=f(x)*f(y) for all x,y anf f(5)=2,f'(0)=3 then f(5) will be

RESONANCE-TEST PAPERS-MATHEMATICS
  1. The number of value(s) of x satisfying 1-log9(x+1)^2=1/2log(sqrt(3))((...

    Text Solution

    |

  2. Total number of ordered pairs (x, y) satisfying Iyl = cos x and y = si...

    Text Solution

    |

  3. If f(x+y)=2f(x) f(y) for all x,y where f'(0)=3 and f'(4)=2, then f'(4)...

    Text Solution

    |

  4. If A is a square matrix such that A(adjA)=[(4,0,0),(0,4,0),(0,0,4)], t...

    Text Solution

    |

  5. Let f(x) be a function whose domain is [-5, 7] and g(x) = |2x + 5|, th...

    Text Solution

    |

  6. f(x)=x^x , x in (0,oo) and let g(x) be inverse of f(x) , then g(x)'...

    Text Solution

    |

  7. Suppose that f is an even, periodic function with period 2,a n dt h a ...

    Text Solution

    |

  8. The value of sin^(-1){cot(sin^(-1)(sqrt((2-sqrt3)/4)+cos^(-1)(sqrt(12)...

    Text Solution

    |

  9. The number of real solutions of cos^-1 x + cos^-1 2 x = -pi is

    Text Solution

    |

  10. If sin^(-1)(tan(pi)/4)-sin^(-1)(sqrt(3/y))-(pi)/6=0 and x^(2)=y then x...

    Text Solution

    |

  11. Find the greatest and least value of (sin^-1x)^3+(cos^-1x)^3.

    Text Solution

    |

  12. The number of ordered triplets (x,y,z) satisfy the equation (sin^(- 1)...

    Text Solution

    |

  13. If y=tan^(-1)x+tan^(-1)(1/x)+cosec^(-1)x,xepsilon(-oo,-1)uu[1,oo), the...

    Text Solution

    |

  14. Find lim(xrarr(2n+1)pi^(+)) sin([sinx](pi)/6), where [.] is a greatest...

    Text Solution

    |

  15. Prove that ("lim")(xvec0)(f(x+h)+f(x-h)-2f(x))/(h^2)=f^(x) (without u...

    Text Solution

    |

  16. lim(xrarr1)(1-x)tan((pix)/2) is equal to

    Text Solution

    |

  17. If f(x)=sqrt(1-e^(-x^2)), then at x=0f(x) is

    Text Solution

    |

  18. If [.] and {.} denote greatest and fractional part functions respectiv...

    Text Solution

    |

  19. If f(x)={((1-sin((3x)/2))/(pi-3x) , x != pi/2),(lambda , x=pi/2)) ...

    Text Solution

    |

  20. If f(x) = lim(n->oo) sum(r=0)^n (tan(x/2^(r+1)) + tan^3 (x/2^(r+1)))/(...

    Text Solution

    |