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Show that the signum function f : R to R...

Show that the signum function `f : R to R` given by:
`f(x) = {{:(1, if x gt 0),(0, if x =0),(-1, if x lt 0):}` is neither one-one nor onto.

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OMEGA PUBLICATION-RELATIONS AND FUNCTIONS -MULTIPLE CHOICE QUESTIONS (MCQs)
  1. Show that the signum function f : R to R given by: f(x) = {{:(1, if ...

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  2. Let the relation in the set {1, 2, 3, 4} given by R= {(1, 2), (2, 2), ...

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  3. Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b...

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  4. Let f:R-R be defined as f(x) = x^4, then (a) f is one-one (b) f is man...

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  5. Let f : R to R be defined as f(x) = 3x. Then a. f is one-one onto b...

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  6. If f : R rarr R be given by: f(x) = (3-x^3)^1//3, then f(f(x)) is:

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  7. Let f : R – {4/3}rarrR be a function defined as f (x) = 4x/(3x+4) T...

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  8. Consider a binary operation ∗ on N defined as a * b = a^3 + b^3 Choose...

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

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

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  11. Number of binary operations on the set {a, b} is :

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  12. Let R be the relation in the set {1,2,3,4} given by: R={(1,2),(2,2),...

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  13. Let R be the relation in the set N given by R ={(a,b) : a = b-2, g gt ...

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

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  15. Let f : R to R be defined as f(x) = 3x. Then a. f is one-one onto b...

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  16. If f : R rarr R be given by: f(x) = (3-x^3)^1//3, then f(f(x)) is:

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  17. Let f : R - {-4/3} rarr R be a function defined as f(x) = (4x)/(3x+4)....

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  18. Consider a binary operation '*' on N defined as a xx b =a^(3) + b^(3)....

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

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

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  21. Number of binary operations on the set {a, b} is :

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