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Functions

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  1. 1.Let f be a polynomial function such that _2(f(x))=( _2(2+(2)/(3)+(2)/(9)+ )) _3(1+(f(x))/(…
  2. 2.Let A=1,2,3,4,5,6.
  3. 3.If the domain of the function f(x)= _(0.6)(|2x-5x^2-4|) is (-,a] b [c,d) (e,), then the va…
  4. 4.Let the domain of the function f(x)= ^-1((4x+5)/(3x-7)) be [ , ] and the domain of g(x)= _…
  5. 5.Let A=(x,y):2x+3y=23,x,y N and B=x:(x,y) A.
  6. 6.If a function f satisfies f(m+n)=f(m)+f(n) for all m,n N and f(1)=1, then the largest natu…
  7. 7.If the range of f( )= ^4 +3 ^2 ^4 + ^2 , R is [ , ], then the sum of the infinite G.P., wh…
  8. 8.If S=a R:|2a-1|=3[a]+2a, where [t] denotes the greatest integer less than or equal to t an…
  9. 9.Consider the function f:R R defined by f(x)=2x√1+9x^2.
  10. 10.Let A=1,2,3, ,7 and let P(A) denote the power set of A.
  11. 11.Let A=1,2,3,4,5 and B=1,2,3,4,5,6.
  12. 12.Let R=a,b,c,d,e and S=1,2,3,4.
  13. 13.If domain of the function _e(6x^2+5x+12x-1)+ ^-1(2x^2-3x+43x-5) is ( , ) ( , ], then 18( ^…
  14. 14.Let A=1,2,3,5,8,9.
  15. 15.Let f:R R be defined as f(x)=2x^2-3x+23x^2+x+3.
  16. 16.Let [ ] denote the greatest integer function.
  17. 17.For the function f:[1,) [1,) defined by f(x)=(x-1)^4+1, among the two statements: (I) The …
  18. 18.Let for some R,f:R R be a function satisfying f(x+y)=f(x)+2y^2+y+ xy for all x,y R.
  19. 19.Let [ ] denote the greatest integer function.
  20. 20.The number of functions f:1,2,3,4 a,b,c, which are not onto, is :
  21. 21.Given below are two statements : Statement I : The function f:R R defined by f(x)=(x)/(1+|…
  22. 22.The sum of all the elements in the range of f(x)=( x)+( x)+( x)+( x), x (n )/(2),n Z
  23. 23.If g(x)=3 x^2+2 x-3, f(0)=-3 and 4 g(f(x))=3 x^2-32 x+72, then f(g(2)) is equal to:
  24. 24.Let f be a function such that 3f(x)+2f((m)/(19x))=5x,x 0, where m= _i=1^9(i)^2.
  25. 25.Consider two sets A=x Z:|(|x-3|-3)| 1 and B=x R-1,2:((x-2)(x-4))/(x-1) _e(|x-2|)=0.
  26. 26.Let f(x)=[x]^2-[x+3]-3,x R, where [.] is the greatest integer funtion.
  27. 27.Let the domain of the function f(x)= _3 _5(7- _2(x^2-10x+85))+ ^-1(|(3x-7)/(17-x)|) be ( ,…
  28. 28.Let f and g be functions satisfying f(x+y)=f(x) f(y), f(1)=7 and g(x+y)=g(x y), g(1)=1, fo…
  29. 29.If the domain of the function f(x)= ^-1((5-x)/(3+2x))+1 _e(10-x) is (-, ] [ , )- , then 6(…
  30. 30.If the range of the function f(x)=5-xx^2-3x+2,x 1,2, is (-, ] [ ,), then ^2+ ^2 is equal t…
  31. 31.Let f,g:(1,) R be defined as f(x)=(2x+3)/(5x+2) and g(x)=(2-3x)/(1-x).
  32. 32.Let f be a function such that f(x)+3f((24)/(x))=4x,x 0.
  33. 33.If the domain of the function f(x)= _7(1- _4(x^2-9x+18)) is ( , ) ( ,o), then + + +o is eq…
  34. 34.f(x)= _e((2x-3)/(5+4x))+ ^-1((4+3x)/(2-x))[ , ) ^2+4
  35. 35.If the domain of the function f(x)=1√10+3x-x^2+1x+|x| is (a,b), then (1+a)^2+b^2 is equal …
  36. 36.If the domain of the function _5(18x-x^2-77) is ( , ) and the domain of the function _(x-1…
  37. 37.Let f:[0,3] A be defined by f(x)=2x^3-15x^2+36x+7 and g:[0,) B be defined by g(x)=x^2025x^…
  38. 38.If f(x)=2^x2^x+√2,x R, then _k=1^81f((k)/(82)) is equal to
  39. 39.Let f:R R be a function defined by f(x)=(2+3a)x^2+((a+2)/(a-1))x+b,a 1.
  40. 40.The function f:(-,) (-,1), defined by f(x)=2^x-2^-x2^x+2^-x is :
  41. 41.Let f(x)=2^x+2+162^2x+1+2^x+4+32.
  42. 42.Let f(x)= _ex and g(x)=x^4-2x^3+3x^2-2x+22x^2-2x+1.
  43. 43.Let A=1,2,3,4 and B=1,4,9,16.
  44. 44.Let the range of the function f(x)=(1)/(2+ 3x+ 3x),x R be [a,b].
  45. 45.If the domain of the function f(x)= ^-1((x-1)/(2x+3)) is R-( , ), then 12 is equal to :
  46. 46.If the function f(x)=((1)/(x))^2x;x>0 attains the maximum value at x=(1)/(e) then :
  47. 47.Let f(x)=(1)/(7- 5x) be a function defined on R.
  48. 48.The function f(x)=x^2+2x-15x^2-4x+9,x R is
  49. 49.Let A=1,3,7,9,11 and B=2,4,5,7,8,10,12.
  50. 50.If the domain of the function f(x)=x^2-25(4-x^2)+ _10(x^2+2x-15) is (-, ) [ ,), then ^2+ ^…