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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)-12`

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DIPTI PUBLICATION ( AP EAMET)-FUNCTIONS-EXERCISE 1A(FUNCTIONS)
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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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  4. If f(x)=log.(1+x)/(1-x) then f((x(1)+x(2))/(1+x(1)x(2)))=

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  5. If f(x)=log.(1-a)/(1+a)" for " 0ltalt1 then f((2a)/(1+a^(2)))=

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  6. If f(a)=log.(2+a)/(2-a)" for " 0lt a lt2 then (1)/(2)f((8a)/(4+a^(2)))...

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  8. For any integer n ge1, the number of positive divisors of n is denoted...

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  9. If NN denotes the set of all positive integers and if f:NN rarrN is d...

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  10. If f(x)=sin[pi^(2)]x+sin[-pi^(2)]x when [x] is the step function, then...

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  11. If f(x) is a polynomial fin x( gt0) satisfying the equation f(x)+f(1//...

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  12. If f(x) is a polynomial function x>0 such that f(x)f(1//x)=f(x)+f(1//x...

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  13. If f(x) is a polynomial function such that f(x)f((1)/(x))=f(x)+f((1)/(...

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  14. If f(x) is a function such that f(x+y)=f(x)f(y) and f(5) =125 " then "...

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  15. If f(x) is a function such that f(xy)=f(x)+f(y) and f(2)=1 then f(x)=

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  16. If f(x)=cos(logx), then show that f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/...

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  20. If f:ArarrR is defined as f(x)=cosx and A={0, pi//6, pi//4, pi//3} the...

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