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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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PSEB-RELATIONS AND FUNCTIONS-Exercise
  1. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 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. Check the injectivity and surjectivity of the following function: f :...

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

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

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  12. Show that the Signum Function f:RrarrR given by f(x) = {(1,,if x>0,,)...

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

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

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

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

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  17. Let A=R-{3} and B=R-{1} . Consider the function f:A–>B. defined by f(x...

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

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  19. Let f : (2, 3, 4, 5} rarr ( 3, 4, 5, 9} and g = (3, 4, 5, 9} rarr (7, ...

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  20. Let f, g and h be functions from R to R. Show that (f + g)oh = foh + g...

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