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Let f:N to Z and f (x)=[{:((x-1)/(2),"wh...

Let `f:N to Z and f (x)=[{:((x-1)/(2),"when x is odd"),(-(x)/(2),"when x is even"):},` then:

A

f (x) is bijective

B

f (x) is injective but not surjective

C

f (x) is not injective but surjective

D

f (x) is neither injective nor subjective

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The correct Answer is:
A
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VK JAISWAL-FUNCTION -SUBJECTIVE TYPE PROBLEMS
  1. Let f:N to Z and f (x)=[{:((x-1)/(2),"when x is odd"),(-(x)/(2),"when ...

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  2. Let f(x) be a polynomial of degree 6 with leading coefficient 2009. Su...

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  3. Let f (x) =x ^(3)-3x Find f (f (x))

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  4. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...

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  5. If the domain of f(x) = sqrt (12-3^(x)-3^(3-x))+ sin ^(-1) ((2x)/(3 ...

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  6. The number of elements in the range of functions: y=sin^(-1) [x^(2)+5/...

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  7. The number of integers in the range of function f(x)= [sinx] + [cosx] ...

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  8. If P (x) is polynomial of degree 4 such than P (-1)=P (1) =5 and P (-2...

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  9. The number of integral vlaue (s) of k for which the curve y = sqrt ( ...

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  10. Let the solution set of the equation sqrt([x+[x/2]])+[sqrt({x})+[x/3]]...

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  11. For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Fi...

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  12. Find the number of elements contained in the range of the function f (...

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  13. Let f (x,y)= x^(2) - y^(2) and g (x,y) = 2xy. such that (f ( x,y))^(2)...

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  14. Let f (x) = (x+5)/(sqrt(x^(2)) +1) AA x in R, then the smallest integr...

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  15. The number of integral vaues of which f : R to R ,f (x) = (x ^(2))/(3)...

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  16. The number of roots of equation ((x-1)(x-3))/((x-2)(x-4))-e^(x)) ((x+1...

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  17. Let f(x)=x^2-bx+c,b is an odd positive integer. Given that f(x)=0 ha...

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  18. Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...

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  19. If f (x) = 4x ^(3) -x ^(2) -2x +1 and g (x) = {{:(min {f(t): 0 le t le...

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  20. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

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  21. Let f x = (ax+b)/(xa+d), where a,b,c d are non zero If f (7) =7,f (11)...

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