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Prove that the function f:N rarrN define...

Prove that the function `f:N rarrN` defined by `f(x)=x^2 +x+ 1` is one -one but not onto.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. If X = {a,b,c,d} and Y = {f,b,d,g}, find X-Y and Y-X.

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  2. Let x = (a,b,c) and Y = (0,1,2,3,4,5), define a one-one function from ...

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  3. Prove that the function f:N rarrN defined by f(x)=x^2 +x+ 1 is one -on...

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  4. Let f, X rarr Y be defined by f(x) = x^2 +1, for all x in X where X =...

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  5. Which of the following functions are one-one? f(x) = 3x + 2

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  6. Which of the following functions are one-one? f(x) = 2x^2 + 3

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  7. Which of the following functions are one-one? f(x) = (1)/(3x-4)

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  8. Whether the following functions is one-one? f(x) = (1)/(x^2) + 1

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  9. Whether the following functions are one-one? f(x) =x + (1)/(x)

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  10. Let A = (-1,1). In each of the following cases, check whether f, A ra...

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  11. Whether the following functions are one-one? f(x) = |x|

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  12. Whether the following functions are one-one? f(x) = x|x|

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  13. Whether the following functions are one-one? f(x) = x^2

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  14. Let f : X rarr Y be defie by f(x) = x^2 for all x in X where X = (-...

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  15. Let f : X rarr Y be defie by f(x = x^2 for all x in X where X = (-2...

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  16. Let f : X rarr Y be defie by f(x = x^2 for all x in X where X = (-2...

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  17. Let f : N rarr N be defined by f (X) = x + 3 for all x in N, obtain f^...

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  18. If f = (5,2),(6,3), g = (2,5),(3,6), write fog.

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  19. Let f : R rarr R be defined by f (x) = x^2 - 3x + 4 for all x in R , ...

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  20. If f (x) = (a-x^n)^(1//n) prove that f(f(x)) = x

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