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Let f : X rarr Y be an invertible functi...

Let `f : X rarr Y` be an invertible function. Show that f has unique inverse.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let f:NrarrN be defined by, f(n) = {((n+1)/2,,if n is odd,,),(n/2,,if ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Show that *:RxxRrarrR, given by (a,b)rarra+4b^2 is a binary operation...

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  16. Let a mapping '*' from R xx R to R be defined by a * b = 2 a + 2 b for...

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  17. Let a binary operation '*' be defined on Z by a * b = 2 a + 2b for all...

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  18. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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  19. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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  20. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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