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Let f : R to R be the signum function d...

Let `f : R to R` be the signum function defined as `f(x) = {{:(1, x gt 0),(0, x =0),(-1, x lt 0):}` and `g: R to R` be the greatest integer function given by `g(x) = [x]` where [x] is greatest integer less than or equal to x. Then, does fog and gof coincide in (0,1] ?

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let A = {1, 2, 3} Then number of relations containing (1, 2) and (1, 3...

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  2. Let A = {1, 2, 3} Then number of equivalence relations containing (1,...

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  3. Let f : R to R be the signum function defined as f(x) = {{:(1, x gt 0...

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  4. Number of binary operations on theset (a,b) is

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  5. Fill in the blank: The number of relations that can be defined from ...

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  6. Let the relation R be defined in N by aRb if 2 a + 3 b = 30. Then R = ...

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  7. Fill in the blank: Consider the set A = (0,1,2) and let R = (0,1), (...

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  8. Let the relation R be defined on the set A={1,2, 3,4,5}" by "R={(a, ...

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  9. Fill in the blank: The identity relation on any non-empty set is alw...

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  10. Fill in the blank: Let f = (1,2), (3,5), (4,1) and g = (2,3), (5,1),...

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  11. Fill in the blank: If f (X) = 4-(x-7)^3, then f^-1 (x) =

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  12. Fill in the blank: If f = (a,c), (b,d) and g = (c, a), (d,b) then ra...

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  13. Fill in the blank: Let f : R rarr R be defined by f(x) = (x)/(sqrt(1...

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  14. Fill in the blank: Let f : R rarr R be defined by f(x) = (1)/(2 + c...

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  15. Fill in the blank: Let * be a binary operation defined on Z as a * b...

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  16. Consider the set A = {1, 2, 3} and R be the smallest equivalence relat...

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  17. Fill in the blank: The domain of the function f : R rarr R defined b...

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  18. Fill in the blank: The total number of injective functions that can ...

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  19. Fill in the blank: Let R1 be the set of all reals except 1 and * be ...

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  20. Let Z be the set of all integers and R be the relation on Z defined as...

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