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Show that the function f : R* rarr R* ...

Show that the function `f : R_* rarr R_*` defined by `f (x) = 1/x` is one-one and onto, where `R_*` is the set of all non-zero real numbers. Is the result true, if the domain `R_*` is replaced by N with co-domain being same as `R_*`?

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MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Let the relation in the set {1, 2, 3, 4} given by R= {(1, 2), (2, 2), ...

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  2. Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b...

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  3. Show that the function f : R* rarr R* defined by f (x) = 1/x is one...

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  4. Check the injectivity and surjectivity of the following function: f ...

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  5. Check the injectivity and surjectivity of the following function: f :...

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  6. Check the injectivity and surjectivity of the following function: f :...

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  7. Check the injectivity and surjectivity of the following function: f ...

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  8. Check the injectivity and surjectivity of the following function: f ...

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  9. Prove that greatest integer function f: RrarrR, given by f (x) = [x], ...

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  10. Prove that Modulus Function f: R rarr R given by : f(x) = | x | is nei...

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  11. Show that the signum function f : R to R given by: f(x) = {{:(1, if ...

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  12. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6...

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  13. In the following case, state whether the function is one-one, onto or ...

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  14. Let A and B be sets, show that f : A xx B rarr B xx A such that f(a,b...

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  15. Let f: N to N be defined by f(n) = {{:((n+1)/2, " if n is odd "),(n/2,...

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  16. Let A =R-{3} and B=R-{1}. Consider the function f : A to B defined by ...

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  17. Let f : R rarr R be defined as f(x) = x^4. Choose the correct answer.

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  18. Let f : RrarrR be defined as f (x) = 3x Choose the correct answer.

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  19. If f:(1,3,4} rarr {1, 2,5} and g:(1,2,5) {1,3} be given by f = {(1, 2)...

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  20. Let f,g and h be function from R to R. Show that (f+g) o h = foh + goh

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