Home
Class 12
MATHS
If f(1) = 1 and f(n + 1) = 2 f(n) + 1, i...

If f(1) = 1 and f(n + 1) = 2 f(n) + 1, if n `ge` 1, then f(n) is.

A

`2^(n+1)`

B

`2^(n)`

C

`2^(n -1 )`

D

`2^(n-1)` - 1

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    DISHA PUBLICATION|Exercise EXERCISE - 1|60 Videos

  • PROBABILITY-1

    DISHA PUBLICATION|Exercise EXERCISE-1 : CONCEPT BUILDER|180 Videos

  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-2: CONCEPT APPLICATOR|30 Videos

Similar Questions

Explore conceptually related problems

Consider the function f defined on the set of all non-negative interger such that f(0) = 1, f(1) =0 and f(n) + f(n-1) = nf(n-1)+(n-1) f(n-2) for n ge 2 , then f(5) is equal to

f (1) = 1, n> = 1f (n + 1) = 2f (n) +1 then f (n) =

Given f(1)=2 and f(n+1)=(f(n)-1)/(f(n)+1)AA n in N then

If a function F is such that F(0)=2 , F(1)=3 , F(n+2)=2F(n)-F(n+1) for n ge 0 , then F(5) is equal to

If f(x) = log ((m(x))/(n(x))), m(1) = n(1) = 1 and m'(1) = n'(1) = 2, " then" f'(1) is equal to

Let f : N rarr R be a function such that f(1) + 2f(2) + 3f(3) + ....+nf(n)= n(n+1) f(n) , for n ge 2 and f(1) = 1 then

Let f:N rarr R be such that f(1)=1 and f(1)+2f(2)+3f(3)+…+nf(n)=n(n+1)f(n), for n ge 2, " then " /(2010f(2010)) is ……….. .

If f(n+2)=(1)/(2){f(n+1)+(9)/(f(n))}, n in N and f(n) gt0 for all n in N , then lim_( n to oo)f(n) is equal to

Let f _(1)(x) =e ^(x) and f _(n+1) (x) =e ^(f _(n)(x))) for any n ge 1, n in N. Then for any fixed n, the vlaue of (d)/(dx) f )(n)(x) equals:

If f(x)=(a-n^(n))^(1//n) where a gt 0 and n in N , then f[f(x)] is equal to :

DISHA PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE - 2
  1. Let f be a function on R given by f(x) = x^(2) and let E = {x in R: - ...

    Text Solution

    |

  2. Let f(x)=x/(1+x^2) and g(x)=(e^-x)/(1+[x]), where [x] is the greatest ...

    Text Solution

    |

  3. The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b)...

    Text Solution

    |

  4. Let f (x) = [x], where [x] denotes the greatest integer less than or e...

    Text Solution

    |

  5. Define relations R(1) and R(2) on set A = [2,3,5,7,10] as xR(1)y is 2x...

    Text Solution

    |

  6. A relation R is defined in the set Z of integers as follows (x, y ) in...

    Text Solution

    |

  7. The domain of the function f(x)=sqrt(x^(2)-5x+6)+sqrt(2x+8-x^(2)) , ...

    Text Solution

    |

  8. The real valued function f(x)=(a^x-1)/(x^n(a^x+1)) is even, then the v...

    Text Solution

    |

  9. the value of the function f(x)=(x^2-3x+2)/(x^2+x-6) lies in the inter...

    Text Solution

    |

  10. The domain of f (x) = log (|x - 2 | - 2 | - 1) is

    Text Solution

    |

  11. If f:R to R satisfies f(x+y)=f(x)+f(y), for all x, y in R and f(1)=7,...

    Text Solution

    |

  12. Find the domain of the following functions: f(x)=sqrt((2/(x^2-x+1)-1/(...

    Text Solution

    |

  13. Which of the following functions is even,

    Text Solution

    |

  14. If f(1) = 1 and f(n + 1) = 2 f(n) + 1, if n ge 1, then f(n) is.

    Text Solution

    |

  15. The range of the function f(x)= (x^2-x+1)/(x^2+x+1) where x in R, is

    Text Solution

    |

  16. Verify that x sgnx=|x| |x|sgnx=x x(sgnx)(sgnx)=x

    Text Solution

    |

  17. The domain of the function f (x) = 3sqrt((x)/(1 - |x|))

    Text Solution

    |

  18. The domain of the function f(x) = sqrt(x^(14) - x^(11) + x^(6) - x^(...

    Text Solution

    |

  19. If f is any function, then (1)/(2) [ f (x) + f(-x) ] is always

    Text Solution

    |

  20. The function f satisfies the functional equation 3f(x)+2f((x+59)/(x1))...

    Text Solution

    |