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Let f : RrarrR , be defined as f(x) = 1...

Let `f : RrarrR` , be defined as `f(x) = 10x + 7`. Find the function `g : RrarrR` such that `g o f = f o g = 1_R`

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. State whether the following statements are true or false. Justify . Fo...

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  2. Consider a binary operation * on N defined as a* b = a^3 + b^3. Then

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

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  4. Let f : W to W be defined as f(n) =n-1, if n is odd and f(n) = n+1, i...

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

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

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  7. Show that the function f : R rarr R given by f (x) = x^3 is injective...

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

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

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

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

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

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

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  15. Consider the binary operations * : R xx R to R and o: R xx R to R def...

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

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

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

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

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

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