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Prove that the greatest integer function...

Prove that the greatest integer function `f : R rarrR` given by `f(x) =[x]` is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Show that f : N rarr N given by f(x) = { ((x +1), if x is odd), ((x ...

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  2. Check the injectivity and surjectivity of the following functions f:...

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  3. Prove that the greatest integer function f : R rarrR given by f(x) =[x...

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  4. Show that the modulus function f: R rarr R given by f(x) = |x|, is nei...

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  5. Show that the signum function f : R rarr R given by f(x)= {(1,if x gt ...

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  6. Let A = {1, 2, 3}, B { 4, 5, 6} and let f = {(1,4),(2,5)(3,6)} be a fu...

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  7. In each of the following cases, states whether the function is one-one...

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  8. Let A and B be sets. Show that f: AxxB to BxxA such that f(a,b) = ...

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

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  10. Let A=R-{3} and B=R-{1} Consider the function f:ArarrB defined by f(x)...

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

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  12. Let f:R rarrR be defined as f(x) = 3x Choose the correct answer

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  13. Let f:{2,3,4,5} rarr {3,4,5,9} and g:{3,4,5,9} rarr{7,11 , 15} be func...

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  14. Find g o f and f o g, if f: R rarr R and g: R rarr R are given by f (x...

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  15. Show that if f: A rarr B and g: B rarr C are one-one, then gof : A rar...

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  16. Show that if f: A rarr B and g: B rarr C are onto, then gof : A rarr C...

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  17. Are 'f' and 'g' both necessarily onto, if gof, is onto?

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  18. Let f:{1 , 2,3 ,} rarr {a, b, c} be one-one, and onto function given b...

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  19. Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. ...

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  20. Consider of f : N rarrN and h : N rarr R defined as f(x) = 2x, g(y) = ...

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