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Functions

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  1. 51.Let f:R R and g:R R be defined as f(x)= array|c|c| _ex, & x>0 e^-x, & x 0 array and g(x)= …
  2. 52.If f(x)=(4x+3)/(6x-4),x (2)/(3) and (f f)(x)=g(x), where g:R-(2)/(3) R-(2)/(3), then (gogo…
  3. 53.If the domain of the function f(x)= _e(2x+34x^2+x-3)+ ^-1((2x-1)/(x+2)) is ( , ], then the…
  4. 54.If the domain of the function f(x)= ^-1((2-|x|)/(4))+ _e(3-x)^-1 is [- , )- , then + + is …
  5. 55.If f(x)= array|c|c| 2+2x, & -1 x<0 1-(x)/(3), & 0 x 3 array;g(x)= array|c|c| -x, & -3 x 0 …
  6. 56.Let f:R-(-1)/(2) R and g:R-(-5)/(2) R be defined as f(x)=(2x+3)/(2x+1) and g(x)=(|x|+1)/(2…
  7. 57.The function f:N-1 N; defined by f(n)= the highest prime factor of n, is :
  8. 58.The range of f(x)=4 ^-1(x^2x^2+1) is
  9. 59.For x R, two real valued functions f(x) and g(x) are such that, g(x)=x+1 and f g(x)=x+3-x.
  10. 60.Let D be the domain of the function f(x)= ^-1( _3x(6+2 _3x-5x)).
  11. 61.The domain of the function f(x)=1[x]^2-3[x]-10 is : ( where [x] denotes the greatest integ…
  12. 62.If f(x)=( 1^ )x+ _e(123)x _e(1234)-( 1^ ),x>0, then the least value of f(f(x))+f(f((4)/(x)…
  13. 63.Let the sets A and B denote the domain and range respectively of the function [f(x)=1 x-x]…
  14. 64.Let f:R-2,6 R be real valued function defined as f(x)=x^2+2x+1x^2-8x+12.
  15. 65.The absolute minimum value, of the function f(x)=|x^2-x+1|+[x^2-x+1], where [t] denotes th…
  16. 66.The range of the function f(x)=√3-x+√2+x is :
  17. 67.The inverse of [y = 5^ x] is :
  18. 68.If f(x)+2f((1)/(x))=3x,x 0, and S=x R:f(x)=f(-x); then S:
  19. 69.If [f:R R] satisfies [f(x + y) = [f(x) + [f(y), for all x, y [ ] R and [f(1) = 7, then [_r…
  20. 70.Domain of definition of the function f(x) = [3 4 - x^2] + [ _10( x^3 - x )], is
  21. 71.The domain of the function [f( x ) = ^ - 1( x - 3 ) 9 - x^2 ]
  22. 72.The graph of the function y = f(x) is symmetrical about the line x = 2, then
  23. 73.If [f:R S], defined by [f( x ) = x - 3 x + 1], is onto, then the interval of S is
  24. 74.Let [f:( - 1,1) B], be a function defined by [f( x ) = ^ - 12x 1 - x^2], then f is both on…
  25. 75.A real valued function f(x) satisfies the functional equation f(x - y) = f(x)f(y) - f(a - …
  26. 76.Let [f:N Y] be a function defined as f(x) = 4x + 3 where Y = y [ ] N, y = 4x + 3 for some …
  27. 77.Let [f( x ) = ( x + 1 )^2 - 1,x - 1] Statement - 1 : The set [ x:f( x ) = f^ - 1( x ) = 0,…
  28. 78.For real x, let f(x) = x3 + 5x + 1, then
  29. 79.The domain of the function f(x) = [1 | x | - x ] is
  30. 80.If f(x)+2 f((1)/(x))=3 x, x 0, and S=x R: f(x)=f(-x); then S:
  31. 81.For x [ ] R, x [ ] 0, Let f0(x) = [1 1 - x] and fn+1 (x) = f0(fn(x)), n = 0, 1, 2, .
  32. 82.The function [f:R [ - 1 2,1 2 ]] defined as [f( x ) = x 1 + x^2], is
  33. 83.Let a, b, c [ R].
  34. 84.Let f(x) = 210.x + 1 and g(x)=310.x - 1.
  35. 85.The function f : N [ ] N defined by f (x) = x - 5 [[ x 5 ],] Where N is the set of natural…
  36. 86.Let f : A [ ] B be a function defined as f(x) = [x - 1 x - 2,] Where A = R - 2 and B = R -…
  37. 87.Let f(x) = ex -- x and g(x) = x2 -- x, [ ] x [ ] R.
  38. 88.Let f(x) = x2 , x [ ] R.
  39. 89.The number of functions f from 1, 2, 3, ...., 20 onto 1, 2, 3, ...., 20 such that f(k) is …
  40. 90.Let fk(x) = [1 k( ^kx + ^kx )] for k = 1, 2, 3, ...
  41. 91.Let f : R [ ] R be defined by f(x) = [x 1 + x^2,x R].
  42. 92.For x [ ] (0, 3/2), let f(x) = [ x ] , g(x) = tan x and h(x) = [1 - x^2 1 + x^2].
  43. 93.Let f(x) = ax (a > 0) be written as f(x) = f1 (x) + f2 (x), where f1 (x) is an even functi…
  44. 94.If [f(x) = _e( 1 - x 1 + x )], [| x | < 1] then [f( 2x 1 + x^2 )] is equal to
  45. 95.The domain of the definition of the function [f(x) = 1 4 - x^2 + _10(x^3 - x)] is
  46. 96.If the function f : R -- 1, --1 [ ] A defined by f(x) = [x^2 1 - x^2] , is surjective, the…
  47. 97.Let A = x [ ] R : x is not a positive integer.
  48. 98.For [x R - 0,1 ], Let f1(x) = [1 x], f2 (x) = 1 -- x and f3 (x) = [1 1 - x] be three given…
  49. 99.Let f : R [ ] R be a function which satisfies f(x + y) = f(x) + f(y) [ ] x, y [ ] R.
  50. 100.For a suitably chosen real constant a, let a function, [f:R - - a R] be defined by [f(x) =…