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If f(1)=1, f(n+1)=2f(n)+1, n ge1, then f...

If `f(1)=1, f(n+1)=2f(n)+1, n ge1`, 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
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AAKASH SERIES-FUNCTIONS -EXERCISE -II
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  2. If f(n)=(-1)^(n-1)(n-1) and g(n)=n-f (n)AA n in N then (gog)(n)=

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  3. If f(1)=1, f(n+1)=2f(n)+1, n ge1, then f(n) is

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  5. If f: R to R is defined by f(x) = x^(2)-3x+2 and f(x^(2)-3x-2) =ax^(4)...

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  6. If f: R to R is defined by: f(x-1) =x^(2) + 3x+2, then f(x-2)=

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  7. The function y=f(x) satisfying the condition f(x+1//x) =x^(3)+1//x^(3...

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  8. If f: N to Z is defined by: f(n) ={{:(2, if, n=3k, k in Z),(10-n, if...

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  9. If f(x) = cos(log x), then f(x^(2)) . f(y^(2)) -1/2[f(x^(2)y^(2)) +f...

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  10. If e^(f(x))=(10+x)/(10-x), x in (-10, 10) and f(x)=kf ((200x)/(100+x^(...

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  11. f(x) = log((1+x)/(1-x)) satisfies the equation: f(x(1)) +f(x(2))

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  12. If f(x) =|x-2| and g(x) = f(f(x)), then for x gt 20, g(x)=

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  13. If f(x) =|x|,g(x)=x then f(x) + g(x) is equal to:

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  14. If f(x) =x and g(x) =|x|, then f(x) + g(x) is equal to

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  15. If f(x)=x^(2) for xlt 0, f(x)=x for 0ltxlt1, f(x)=1//x for x gt1 then ...

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  16. Suppose f:[-2, 2] rarr RR is defined by f(x)={{:(-1" for "-2 le x le 0...

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  17. If g[f(x)]=|sinx|, f[g(x)]=(sinsqrtx)^(2) then

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  18. If f(x) = cos|e^(2)| x + cos[-e^(2)]x where [x] stands for greatest in...

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  19. If f:RR rarr RR is defined by f(x)=x-[x] -(1)/(2)" for "x in RR, where...

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  20. Let g(x) =1+x-[x] and f(x) ={{:(-1, if, x lt 0),(0, if, x=0),(1, if, x...

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