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Consider f:NrarrN, g: NrarrN and h:Nrarr...

Consider `f:NrarrN`, `g: NrarrN` and `h:NrarrR` defined as `f(x) = 2x`, `g(y) = 3y + 4` and `h(z) = sin z, forall x, y and z` Show that `ho(gof) = (hog)of`.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. If f(x) = 2x + 3 and g (X) = x^2 + 1, describe the functions fof Also ...

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  2. If f(x) = 2x + 3 and g (X) = x^2 + 1, describe the functions ff. Also ...

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  3. Consider f:NrarrN, g: NrarrN and h:NrarrR defined as f(x) = 2x, g(y) =...

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  4. Consider f:(1,2,3) rarr (a,b,c) and g:(a,,c) rarr (apple, ball, cat) d...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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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