Home
Class 11
MATHS
Let f : R to R be a function defined by ...

Let `f : R to R` be a function defined by `f (x + y) = f (x).f (y) and f (x) ne 0` for andy `x. If f '(0)` exists, show that `f '(x) = f (x). F'(0) AA x in R if f '(0) = log 2` find `f (x).`

Text Solution

Verified by Experts

The correct Answer is:
`f (x)= 2 ^(x)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    AAKASH SERIES|Exercise EXERCISE -4.7|25 Videos
  • CONTINUITY

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS|34 Videos
  • DIFFRENTATION

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (PRACTICE SHEET (ADVANCED)) (Integer Type Questions)|5 Videos

Similar Questions

Explore conceptually related problems

f : R to (0, oo) defined by f (x) = 2 ^(x) . then f ^-1(x)

If 'f is a function such that f (x + y) =f (x) f (y) for all x,y in R and f ^(1) (0) exists, show that f ^(1) (x) = f(x) f ^(1)(0) for all x, y in R.

f : R to (0, oo) defined by f (x) = log _(2) (x). then f ^-1(x)

If f (x-y), f (x) ,f (y) and f (x + y) are in A.P for all x,y in E and f (0) = 0 show that f ' (x) is even.

Let f : R to R be defined by f (x + y) = f (x) - f (y) + 2xy + 1 AA x, y in R . If f (x) is differentiable every where and f '(0) =1, find f '(x).

Let a fiunction f defined by f(x)=(x-|x|)/(x) "for" x ne0 and f(0) =2 then f is

If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

If f: R to R is defined by f(x) = 2x+|x| , then f(3x) -f(-x)-4x=

AAKASH SERIES-DIFFERENTIATION -ADVANCED SUBJECTIVE TYPE QUESTIONS
  1. The number of cirtical points of the function f(x)=|x|e^(-x) must be

    Text Solution

    |

  2. If f (x-y), f (x) ,f (y) and f (x + y) are in A.P for all x,y in E an...

    Text Solution

    |

  3. Let f : R to R be a function defined by f (x + y) = f (x).f (y) and f ...

    Text Solution

    |

  4. If f (x +y) = 2 f (x) .f(y) such that f '(0) 3 and (4) = 2 find d'(4)...

    Text Solution

    |

  5. Let f : R to R be defined by f (x + y) = f (x) - f (y) + 2xy + 1 AA x,...

    Text Solution

    |

  6. If f (x) is a function such that (x - y) f (x + y)- (x + y) f (x - y) ...

    Text Solution

    |

  7. Show that (d ^(2)x)/( dy^2) =- ((d ^(2) y )/( dx ^(2))) ((dy)/(dx)) ^(...

    Text Solution

    |

  8. If f (x) = {{:((x ^(2))/( 2 ) "," , 0 le x lt 1), (2x ^(2) - 3x + (3)/...

    Text Solution

    |

  9. Show that the function f (x) = |x-1|+ | x- 2| is not differentiable at...

    Text Solution

    |

  10. Prove theat the greatest interger function defined by f(x)= |x|, 0 lt ...

    Text Solution

    |

  11. Show that the function f (x) = {{:( x, if x lt 1), ( 6 -2x , if 1 le x...

    Text Solution

    |

  12. If 'f is a function such that f (x + y) =f (x) f (y) for all x,y in R ...

    Text Solution

    |

  13. If f (x) = ax ^(2) + bx + c then find Lt (x to 5) (f (x) - f (5))/(x-...

    Text Solution

    |

  14. If f (x) has a derivative at x =a then find Lt (x to a) (x f (a) - a f...

    Text Solution

    |

  15. Prove that f (x) = x |x| is differentiable at x =0 and find f'(0) als...

    Text Solution

    |

  16. Show that the function f (x) = (x)/(1 + |x| ) , x in R, is differentia...

    Text Solution

    |

  17. Show that the functions f (x) = x ^(3) sin ((1)/(x)) for x ne 0, f (0)...

    Text Solution

    |

  18. If f (x) = (x -1)/( 2x ^(2) - 7x + 5) for x ne 1, f (1) = (-1)/(3), fi...

    Text Solution

    |

  19. For the function f(x)=(x^(100))/(100)+(x^(99))/(99)+….+(x^(2))/(2)+x...

    Text Solution

    |

  20. If f (x) = f ^(1) (x) + f ^(11) (x) + f ^(111) (x) +........oo then f...

    Text Solution

    |