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Let f : WrarrW, be defined as f (n) = n...

Let `f : WrarrW`, be defined as `f (n) = n – 1`, if n is odd and `f (n) = n + 1`, if n is even. Show that `f` is invertible. Find the inverse of `f`. Here, `W` is the set of all whole numbers.

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MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Consider a binary operation ∗ on N defined as a * b = a^3 + b^3 Choose...

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  2. Let f : RrarrR , be defined as f(x) = 10x + 7. Find the function g : ...

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  3. Let f : WrarrW, be defined as f (n) = n – 1, if n is odd and f (n) = ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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