Home
Class 12
MATHS
Let f :R to R be a continous and differe...

Let `f :R to R` be a continous and differentiable function such that `f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2.`
Let `f (xy) =g (x). G (y) AA x, y and g'(1)=2.g (1) ne =0`
Identify the correct option:

A

`g (2) =2`

B

`g (3)=3`

C

`g (3)=9`

D

`g (3) =6`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATHCING TYPE PROBLEMS)|3 Videos

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|24 Videos

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|36 Videos

  • COMPOUND ANGLES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|31 Videos

  • DETERMINANTS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let g (xy) =g (x). g (y) AA x, y and g'(1)=2.g (1) ne =0 Identify the correct option:

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let g (xy) =g (x). g (y) AA x, y and g'(1)=2.g (1) ne =0 The number of values of x, where f (x) g(x):

Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f(x) be a differentiable function on x in R such that f(x+y)=f(x). F(y)" for all, "x,y . If f(0) ne 0, f(5)=12 and f'(0)=16 , then f'(5) is equal to

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

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

VIKAS GUPTA (BLACK BOOK) ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (COMPREHENSION TYPE PROBLEMS)
  1. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

    Text Solution

    |

  2. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

    Text Solution

    |

  3. Let f (x)= {{:(x [x] , 0 le x lt 2),( (x-1), 2 le x le 3):} where [x]=...

    Text Solution

    |

  4. Let f :R to R be a continous and differentiable function such that f (...

    Text Solution

    |

  5. Let f :R to R be a continous and differentiable function such that f (...

    Text Solution

    |

  6. Let f :R to R be a continous and differentiable function such that f (...

    Text Solution

    |

  7. Let f (x) (cos ^(2) x)/(1+ cos +cos ^(2)x )and g (x) lamda tan x+1(1-l...

    Text Solution

    |

  8. Let f (x) = (cos ^(2) x)/(1+ cos x+cos ^(2)x )and g (x) =lamda tan x+(...

    Text Solution

    |

  9. Population evolve to maximize their reproductive potential in the habi...

    Text Solution

    |

  10. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

    Text Solution

    |

  11. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

    Text Solution

    |

  12. Let f and g be two differentiable functins such that: f (x)=g '(1) s...

    Text Solution

    |

  13. Suppose a function f(x) satisfies the following conditions f (x+y) =...

    Text Solution

    |

  14. Suppose a function f(x) satisfies the following conditions f (x+y) =...

    Text Solution

    |

  15. Let f (x) be a polynomial satisfying lim (x to oo) (x ^(4) f (x))/( x ...

    Text Solution

    |

  16. Let f (x) be a polynomial satisfying lim (x to oo) (x ^(4) f (x))/( x ...

    Text Solution

    |

  17. Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta b...

    Text Solution

    |

  18. Consider f (x) = x ^(ln x), and g (x) = e ^(2) x. Let alpha and beta b...

    Text Solution

    |

  19. Let f (n) x+ f (n) (y ) = (x ^(n)+y ^(n))/(x ^(n) y ^(n))AA x, y in R-...

    Text Solution

    |

  20. Let f (n) x+ f (n) (y ) = (x ^(n)+y ^(n))/(x ^(n) y ^(n))AA x, y in R-...

    Text Solution

    |