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If RR rarrC is defined by f(x)=e^(2ix)" ...

If `RR rarrC` is defined by `f(x)=e^(2ix)" for x in RR` then, f is (where C denotes the set of all complex numbers)

A

one-one

B

onto

C

one-to-one and onto

D

neither one-one nor onto

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The correct Answer is:
D
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SIA PUBLICATION-FUNCTIONS AND MATHEMATICAL INDUCTION -Problems
  1. {x in RR:(2x-1)/(x^(3)+4x^(2)+3x) in RR}=

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  2. Using mathematical induction, the numbers a(n)'s are defined by, a...

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  3. If RR rarrC is defined by f(x)=e^(2ix)" for x in RR then, f is (where ...

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  4. If f:[-6, 6]rarr RR defined by f(x)=x^(2)-3" for " x in R then (fofof...

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  5. If f:Rrrarr RR and g: RR rarr RR are defined by f(x)=|x| and g(x)=[x-3...

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  6. For any integer n ge 1 , the sum sum(k=1)^(n)k(k+2) is equal to

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  7. If f:R rarr R is defined by f(x)=(1)/(2-cos 3x) for each x in R then t...

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  8. If f : R to R and g : R to R are defined by f(x)=x-{x} and g(x)=[x] fo...

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  9. If S(n)=1^(3)+2^(3)+…+n^(3) and T(n)=1+2+….+n, then

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

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  11. If f:R rarr R is defined by f(x)=[2x]-2[x] for x in R, then the range ...

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  12. If f : R to R is defined by f(x) = {{:(x+4" for " x lt - 4),(3x+2" ...

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  13. For all integers, n ge 1 which of the following is divisible by 9.

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  14. {x in R : [x-|x|=5} is equal to

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  15. The function f : C to C defined by f(x)=(ax+b)/(cx+d) for x in C, whe...

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  16. If N denotes the set of all positive integers and if f : N to N is def...

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  17. {n(n+1)(2n+1):n in 1} sub

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  18. If f : N to Z is defined by f(x)={{:("2 if "n = 3k" , " k ...

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  19. The function f:R rarrR is defined by f(x)=3^(-x). Observe the followin...

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  20. If n in N , and the period of (cos nx)/(sin(x//n)) is 4pi , then n=

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