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Define f:Z rarrZ by f(x)={{:(x//2,"(x is...

Define `f:Z rarrZ` by `f(x)={{:(x//2,"(x is even)"),(0,"(x is odd)"):}` then f is

A

onto but not one-one

B

one-one but not onto

C

one-one and onto

D

neither one-one nor onto

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The correct Answer is:
A
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AAKASH SERIES-FUNCTIONS -EXERCISE -I
  1. The function f: N to N defined by f(n) =2n+3 is

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  2. f: N to A where N is the set of natural numbers and A is the set of e...

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  3. Define f:Z rarrZ by f(x)={{:(x//2,"(x is even)"),(0,"(x is odd)"):} th...

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  4. If f:[0,infty) to R defined by f(x) = x^(2), then f is

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  5. Let X and Y be subsets of R, the set of all real numbers. The function...

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  6. If f: A to A is defined by f(x) =x^(3), where A ={x//-1 le x le 1}, th...

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  7. The function cos(3x-4) defined from R to R is:

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  8. A is a finite set and B is a singleton set. Then f: A to B is:

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  9. Set A has n elements. The number of functions that can be defined from...

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  10. The number of one one functions that can be defined from {1, 2, 3, 4}...

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  11. Let n(A) = 4 and n(B) = k. The number of all possible injections from ...

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  12. Let n(A) = 4 and n(B) = 5. The number of all possible many-one functio...

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  13. Set A contains 3 elements and set R contains 2 elements. The number of...

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  14. Let A = {1, 2, 3,--------n} and B = {a, b, c], the number of functions...

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  15. Set A has 3 elements. Set B has 4 elements. The number of surjections ...

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  16. If A = {a(1),a(2), ……,a(10)} and B = {b(1),b(2),b(3),…….b(10)} then th...

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  17. The number of one one onto functions that can be defined from {1,2,3,4...

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  18. If A, B are two sets such that n(A) = 100, n(B) = 150, then the number...

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  19. A = {1, 2, 3, 4), B = {a, b, c, d, e}, then the number of all possible...

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  20. If A = {1, 2, 3, 4} then the number of binary operations that can be d...

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