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Functions

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  1. 101.If f(x + y) = f(x)f(y) and [_x = 1^ f( x ) = 2] , x, y [ ] N, where N is the set of all na…
  2. 102.If g(x) = x2 + x - 1 and (gof) (x) = 4x2 - 10x + 5, then f[( 5 4 )] is equal to:
  3. 103.The inverse function of f(x) = [8^2x - 8^ - 2x 8^2x + 8^ - 2x], x [ ] (-1, 1), is :
  4. 104.Let a -- 2b + c = 1.
  5. 105.The range of a[]R for which the function f(x) = (4a - 3)(x + loge 5) + 2(a - 7) cot[( x 2 …
  6. 106.Let f : R - 3 [ ] R - 1 be defined by f(x) = [x - 2 x - 3].
  7. 107.The real valued function [f(x) = ec^ - 1x x - [x] ], where [x] denotes the greatest intege…
  8. 108.If the functions are defined as [f(x) = x ] and [g(x) = 1 - x ], then what is the common d…
  9. 109.The range of the function, [f(x) = _ 5 ( 3 + ( 3 4 + x ) + ( 4 + x ) + ( 4 - x ) - ( 3 4 -…
  10. 110.Let [f:R - 6 R] be defined by [f(x) = 5x + 3 6x - ].
  11. 111.Let [ x ] denote the greatest integer [] x, where x [] R.
  12. 112.Let f : R R be defined as f (x) = 2x -- 1 and g : R - 1 R be defined as g(x) = [x - 1 2 x …
  13. 113.A function f(x) is given by [f(x) = 5^x 5^x + 5], then the sum of the series [f( 1 20 ) + …
  14. 114.Let x denote the total number of one-one functions from a set A with 3 elements to a set B…
  15. 115.Let f, g : N [ ] N such that f(n + 1) = f(n) + f(1) [ ] n[]N and g be any arbitrary functi…
  16. 116.Consider function f : A [] B and g : B [] C (A, B, C [ ] R) such that (gof)-1 exists, then…
  17. 117.Let g : N [] N be defined as g(3n + 1) = 3n + 2, g(3n + 2) = 3n + 3, g(3n + 3) = 3n + 1, f…
  18. 118.Let [A = 1,2,3,....,10 ] and [f:A A] be defined as [f(k) = pmatrix k + 1 & if,k,is,odd k &…
  19. 119.Let f : R [] R be defined as [f(x + y) + f(x - y) = 2f(x)f(y),f( 1 2 ) = - 1].
  20. 120.Let f : N [] N be a function such that f(m + n) = f(m) + f(n) for every m, n[]N.
  21. 121.The number of bijective functions [f:1,3,5,7, , 99 2,4,6,8, .100], such that [f(3) f(9) f(…
  22. 122.The total number of functions, [ f:1,2,3,4 1,2,3,4,5,6 ] such that f(1)+f(2)=f(3), is equa…
  23. 123.Let f : N [] R be a function such that f(x + y) = 2f(x)f(y) for natural numbers x and y.
  24. 124.Let [f:R R] and [g:R R] be two functions defined by [f(x) = _e(x^2 + 1) - e^ - x + 1] and …
  25. 125.Let f : R [] R be defined as f (x) = x - 1 and g : R - 1, -1 [] R be defined as [g(x) = x^…
  26. 126.Let [f(x) = x - 1 x + 1,,x R - 0, - 1,1 ].
  27. 127.Let [f, g: N-1 N] be functions defined by [f(a)=], where [] is the maximum of the powers o…
  28. 128.[ Let f(x)=a x^2+b x+c be such that f(1)=3, f(-2)= and ] f(3)=4.
  29. 129.Let [, ] and [] be three positive real numbers.
  30. 130.Let [D] be the domain of the function [f(x)= ^-1( _3 x(6+2 _3 x-5 x))].
  31. 131.Let [f:R-0,1 R] be a function such that [f(x)+f((1)/(1-x))=1+x].
  32. 132.Let f(x) be a function such that f(x+y)=f(x).f(y) for all [x,y N].
  33. 133.If [f(x) = 2^2x 2^2x + 2,x R], then [f( 1 2023 ) + f( 2 2023 ), + ,..., + ,f( 2022 2023 )]…
  34. 134.The number of functions [f: 1,2,3,4 a Z|a| 8 ] satisfying [f(n) + 1 nf(n + 1) = 1, n 1,2,3…
  35. 135.Let [f:RR] be a function defined by [f(x) = _ m 2 ( x - x) + m - 2 ], for some m, such tha…
  36. 136.Let [f(x) = 2x^n + , R,n N], and f(4) = 133,f(5) = 255.
  37. 137.Consider a function [f:NR], satisfying [f(1)+2f(2)+3f(3)+....+xf(x)=x(x+1)f(x);x2] with f(…
  38. 138.The domain of [f(x) = _(x + 1)(x - 2) e^2 _ex - (2x + 3),x R] is
  39. 139.Let [f:R R] be a function such that [f(x) = x^2 + 2x + 1 x^2 + 1].
  40. 140.Let f: R-2,6 R be real valued function defined as f(x)=(x^2+2 x+1)/(x^2-8 x+12).
  41. 141.If the domain of the function [f(x)=[x]1+x^2], where [[x]] is greatest integer [ x], is [[…
  42. 142.Let the sets A and B denote the domain and range respectively of the function [f(x)=1 x-x]…
  43. 143.If the domain of the function f(x)=x^2-25(4-x^2)+ _10(x^2+2 x-15) is (-, ) [, ), then ^2+^…
  44. 144.Let [f: R-(-1)/(2) R] and [g: R-(-5)/(2) R] be defined as [f(x)=(2 x+3)/(2 x+1)] and [g(x)…
  45. 145.If the domain of the function [f(x)= _e((2 x+3)/(4 x^2+x-3))+ ^-1((2 x-1)/(x+2))] is [(, ]…
  46. 146.If [f(x)=(4 x+3)/(6 x-4), x (2)/(3)] and [(f f)(x)=g(x)], where [g: R-(2)/(3) R-(2)/(3)], …
  47. 147.Let [f, g: R R] be defined as : [f(x)=|x-1| and g(x)= casese^x, & x 0 x+1, & x 0 .cases] T…
  48. 148.Let [f(x)=(1)/(7- 5 x)] be a function defined on [R].
  49. 149.The function [f(x)=(x^2+2 x-15)/(x^2-4 x+9), x R] is
  50. 150.Let the range of the function [f(x)=(1)/(2+ 3 x+ 3 x), x R] be [[a, b]].