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Check the injectivity and surjectivity of the following function: `f : NrarrN` given by `f(x) = x^2`

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PSEB-RELATIONS AND FUNCTIONS-Exercise
  1. Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b...

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

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

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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:RrarrR given by f(x) = {(1,,if x>0,,)...

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

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

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

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

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

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

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

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

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  20. Find gof and fog, if f(x) = |x| and g(x) = |5x -2|

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