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Explain why the following functions f : ...

Explain why the following functions f : `X rarr Y` do not have inverses:
X= R = Y and f (X) =`x^2` for all x `in` R.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Explain why the following functions f : X rarr Y do not have inverses:...

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  2. Explain why the following functions f : X rarr Y do not have inverses:...

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  3. Explain why the following functions f : X rarr Y do not have inverses:...

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  4. If A = (a,b,c,d) and f corresponds to the subset (a,b),(b,d),(c,a),(d,...

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  5. Let f : Z rarr Z be defined as f(n) = 3n for all n in Z. Let g : Z ra...

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  6. Let f : R rarr R be defined by f(x) = 1/x AA x inR, then f is

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  7. Let f:NrarrN be defined by, f(n) = {((n+1)/2,,if n is odd,,),(n/2,,if ...

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  8. Lert f : X rarr Y be such that fof = f. Show that f is onto if and onl...

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  9. Let f : X rarr Y be an invertible function. Show that f has unique inv...

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  10. Let A be any non-empty set and f be a bijection on A, prove that f^-1 ...

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  11. Let A be any non-empty set and f be a bijection on A, prove that f^-1 ...

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  12. Let f : A rarr B and g : B rarr C be onto functions, show that gof is ...

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  13. Consider f: Rrarr[-5, oo] given by f(x) = 9x^2 + 6x - 5. Show that f ...

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  14. Consider f : R+ rarr (-9, infty) given by f(x) = 5x^2 + 6x - 9. Prove ...

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

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  16. Let f: R rarr R be defined as f(X) = 3x. Then

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  17. Consider the function f(x) = (1-x)/(1+x). Is f one-one? If yes, find f...

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

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

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

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