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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 correct Answer is:
One - One and onto
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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Practice Work
  1. Check the injectivity and surjectivity of the following functions . ...

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

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

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  4. f:Z rarrZ , f(n) ={{:((n+2)," if n is even"),((2n+1)," if n is odd" )...

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  5. f:NxxNrarrN , f("(m,n)")=m+n . If f one one and onto ?

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  6. Show that f: R rarr R , f(x) = x/(x^(2)+1) is not one one and onto fun...

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  7. f: R rarr R , f(x) =x^(2)+1. Find the preimage of 17 and -3.

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  8. f : R rarr R , f(x) ={{:(2x,xgt3),(x^2,1ltxle3),(3x,xle1):} then find...

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  9. Is g= {(1, 1), (2,3), (3,5), (4,7)} a function, justify. If this is de...

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  10. The functions f and g are defined as follow : f = {(1,2),(3,5),(4,1) }...

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  11. For functions f: A rarr B and g : B rarr A , gof = IA . Prove that f i...

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  12. f: R rarr R , f(x) = x^(2)+2 and g :R rarr R , g (x) = x/(x-1) then f...

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  13. f: N rarr R , f(x) = 4x^(2) +12x +5. Show that f: N rarr R is invertib...

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  14. f and g are real valued function f(x) =x^(2) + x + 7 , x in R and g(x)...

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  15. If f is greatest integer function and g is a modulus functions the fin...

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  16. f:R rarrR , f(x) =x/(sqrt(1+x^2)),AAx inR. Then find (fofof) (x).

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  17. f : Z rarr Z and g : Z rarr Z. Defined as f(n) = 3n and g(n) = {{:(n/3...

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  18. f: R rarrR be defined by f(x) =x/2+3, g: R rarr R be defined by g(x) ...

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  19. f: Z rarrZ and g : Z rarrZ are defined as follow : f(n) ={:{(n+2," n...

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  20. ** is a binary operation on the set Q. a"*"b = (2a+b)/4 then find 2"...

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