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Show that the function f : Rrarr {x in R...

Show that the function `f : Rrarr {x in R : – 1 < x < 1}` defined by `f(x)=x/(1+|x|), x in R` is one one and onto function.

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MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Let f : WrarrW, be defined as f (n) = n – 1, if n is odd and f (n) = ...

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

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  3. Show that the function f : Rrarr {x in R : – 1 < x < 1} defined by f(x...

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  4. Show that the function f : R rarr R given by f(x) =x^2 is injective.

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  5. Give examples of two functions f : NrarrZ and g : ZrarrZ such that g ...

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  6. Give examples of two functions f : NrarrN and g : NrarrN such that g o...

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  7. Given a non empty set X, consider P(X) which is the set of all subsets...

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

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  9. Find the number of all onto functions formthe set {1,2,3,….,n} to itse...

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  10. Let S = {a,b,c} and T = {1,2,3}. Find F^-1 of the folowing functions F...

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  11. Let S = {a,b,c} and T = {1,2,3}. Find F^-1 of the folowing functions F...

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  12. Consider the binary operations * : RxxRrarrR and o : RxxRrarrR define...

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  13. Given a non-empty set X, let * : P(X)xxP(X)rarrP(X), be defined as A *...

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  14. Define a binary operation * on the set {0,1,2,3,4,5} as a*b = {:{(a+...

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  15. Let A = {– 1, 0, 1, 2}, B = {– 4, – 2, 0, 2} and f, g : A rarr B, be f...

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

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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 to R be the signum function defined as f(x) = {{:(1, x gt 0...

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  19. Number of binary operations on theset (a,b) is

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  20. Show that if A= { 1,2,3} and R ={(1,1),(2,2),(3,3) (1,2),(2,1),(2,3),...

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