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Show that the function f : R rarr {x inR...

Show that the function `f : R rarr {x inR:-1lt x lt1}` defined by `f(x) =x/(1+|x|),x in R` is one one and onto function.

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`:.` The function f is onto.
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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -MISCELLANEOUS EXERCISE - 1
  1. Let f : R rarr R be defined as f(x) = 10 x +7. Find the function g:R r...

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  2. Let f:W rarrW be defined as f(n) = n - 1, if n is odd and f(n) = n + 1...

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  3. If f: R rarrR is defined by f(x) =x^(2)-3x+2 , find f(f(x)).

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  4. Show that the function f : R rarr {x inR:-1lt x lt1} defined by f(x) ...

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  5. Show that the function f : R rarr R given by f(x) =x^(3) is injectiv...

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  6. Give examples of two functions f:N rarr Z and g: Z rarr Z such that go...

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  7. Give examples of two function f: N rarr N and g : N rarr N such that g...

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  8. Given a non empty set X , consider P(X) which is the set of all subset...

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  9. Given a non - empty set, X , consider the binary operation ** : P(X) x...

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  10. Find the number of all onto functions from the set {1,2,3,.......,n} t...

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  11. Let S = {a,b,c} and T = {1,2,3} . Find F^(-1) of the following functio...

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  12. Let S = {a,b,c} and T = {1,2,3} . Find F^(-1) of the following functio...

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  13. Consider the binary operations ** R xx R rarrR and o : RxxR rarrR defi...

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  14. Given a non - empty set X , let **:P(X) xxP(X) rarr P(X) be defined ...

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  15. Define a binary operation ** on the set {0,1,2,3,4,5} as a**b={{:(a+b"...

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  16. Let A = {-1,0,1,2}, B = {-4,-2,0,2} and f , g : A rarr B be functions ...

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

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

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  19. Let f : R rarr R be the Signum Function defined as f(x) = {(1,xgt0),(...

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  20. Number of binary operations on the set {a,b} are

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