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Give examples of two functions `f:" "N->Z" "a n dg:" "Z->Z` such that o f is injective but is not injective. (Hint: Consider `f(x)" "=" "x" "a n d""""""""g(x)" "=" "|x|` )

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Misellaneous Exercise on Chapter (1)
  1. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

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  2. Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...

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  3. If f: R ->Ris defined by f(x) = x^2- 3x + 2, find f(f(x)).

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  4. Show that function f: R ->{x in R : -1 < x < 1}defined by f(x)=x/(1+...

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  5. Show that the function f: R->Rgiven by f(x)=x^3is injective.

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  6. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

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  7. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

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  8. Given a non-empty set X , consider P\ (X) which is the set of all subj...

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  9. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

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  10. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

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  11. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

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  12. Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R de...

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  13. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

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  14. Define a binary operation *on the set {0," "1," "2," "3," "4," "5} as ...

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  15. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

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  16. Let A={1,2,3}. Then the number of relations containing (1,2) and (1,3)...

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  17. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

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  18. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

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  19. समुच्चय {a,b} में द्विआधारी संक्रियाओं की संख्या है :

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