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Show that f : R to R defined as f(x) = s...

Show that `f : R to R` defined as `f(x) = sgn(x)` is neither one-one nor onto.

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MODERN PUBLICATION-RELATION AND FUNCTIONS-EXERCISE
  1. Find three positive integers x(i),i = I, 2, 3 satisfying 3x = 2 (mod 7...

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  2. State the reason for the relation R in the set {1, 2, 3} given by R ={...

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  3. Show that f : R to R defined as f(x) = sgn(x) is neither one-one nor o...

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  4. Give an example of a function which is injective but not surjective.

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  5. Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)} Determine gof ...

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  6. Express each of the following function as the sum of an even function ...

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  7. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  8. If the invertible function f is defined as f(X) = (3x-4)/5 , write f^(...

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  9. Let f , R to R and g , R to R defined as f(x) = | x |, g(x) = | 5x - 2...

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  10. Let * is a binary operation defined by a * b = 3a + 4b - 2, find 4*5.

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  11. Let the binary operation on Q defined as a * b = 2a + b - ab, find 3*4...

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  12. Let * is a binary operation on Z defined as a * b = a + b - 5 find the...

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  13. Find the number of binary operations on the set {a, b}.

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  14. Let * is a binary operation on [0, ¥) defined as a * b = sqrt (a^(2)+b...

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  15. List the members of the equivalence relation defined by {{1},{2},{3,4...

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  16. Find least non negative integer r such that 7xx13xx23xx413 -= r "(mod ...

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  17. Find least non negative integer r such that 1237"(mod 4)"+985"(mod 4)"...

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  18. For real numbers x and y, define x R y if and only if x-y +sqrt(2) is ...

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  19. Let A = {a,b,c) and the relation R be defined on A as follows: R={{a...

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  20. Let X and Y be sets containing m and n elements respectively.How many ...

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