Home
Class 12
MATHS
The domain of definition of the function...

The domain of definition of the function `f(x)={x}^({x})+[x]^([x])` is where `{dot}` represents fractional part and `[dot]` represent greatest integral function). `R-I` (b) `R-[0,1]` `R-{Iuu(0,1)}` (d) `Iuu(0,1)`

A

`R-I`

B

`R-{0,1)`

C

`R-{I cup (0,1)}`

D

`I cup (0,1)`

Text Solution

Verified by Experts

The correct Answer is:
C
` f(x)={x}^({x})+[x]^([x])`
Here, base {x} and [x] should not be zero.
Hence, ` x notin I " and " x notin [0,1).`
Thus, domain is `R-{I cup (0,1)}.`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

The domain of definition of the function f(x)={x}^({x})+[x]^([x]) is where {.} represents fractional part and [.] represent greatest integral function).(a)R -I(b)R-[0,1]R-{I uu(0,1)}(d)I uu(0,1)

Domain of the function f(x)=log_(e)cos^(-1){sqrt(x)}, where {.} represents fractional part function

The domain of definition of the function f(x)=(1)/(sqrt(x-[x])), where [.] denotes the greatest integer function,is:

The domain of the function f(x)=(1)/(sqrt({x}))-ln(x-2{x}) is (where {.} denotes the fractional part function)

Find the range of f(x)=[sin{x}], where {} represents the fractional part function and [] represents the greatest integer function. A. -1 B. 0 C. 1 D. 0.5

If domain of f(x) is (-oo,0], then domain of f(6{x}^(2)-5(x)+1) is (where {.} represents fractional part function)

The domain of definition of the function f(x)="log"|x| is R b. (-oo,0) c. (0,oo) d. R-{0}

The domain of the function f(x)=(1)/(sqrt([x]^(2)-[x]-20)) is (where, [.] represents the greatest integer function)

If domain of f(x) is (-prop, 0) then domain of f(6{x}^2- 5 {x} + 1) is (where {*} represetns fractional part function)

The number of solution of the equation sgn({x})=|1-x| is/are (where {*} represent fractional part function and sgn represent signum function)

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. The range of f(x)=(x+1)(x+2)(x+3)(x+4)+5 for x in [-6,6] is

    Text Solution

    |

  2. The range of f(x)=sec^(-1)((log)3tanx+(log)(tanx)3) is

    Text Solution

    |

  3. The domain of definition of the function f(x)={x}^({x})+[x]^([x]) is w...

    Text Solution

    |

  4. 49. If [x^2-2x + a] = 0 has no solution then

    Text Solution

    |

  5. If [x] and {x} represetnt the integral and fractional parts of x , res...

    Text Solution

    |

  6. If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest inte...

    Text Solution

    |

  7. Let f(x)=([a]^2-5[a]+4)x^3-(6{a}^2-5{a}+1)x-(tanx)xsgnx be an even fun...

    Text Solution

    |

  8. The solution set for [x]{x}=1 (where {x} and [x] are respectively, fra...

    Text Solution

    |

  9. Let [x] represent the greatest integer less than or equal to x If [sqr...

    Text Solution

    |

  10. The number of roots of x^2-2=[sinx],w h e r e[dot] stands for the grea...

    Text Solution

    |

  11. The domain of f(x)=sin^(-1)[2x^2-3],w h e r e[dot] denotes the greates...

    Text Solution

    |

  12. The domain of f(x)=sqrt(2{x}^2-3{x}+1), where {.} denotes the fraction...

    Text Solution

    |

  13. The range of sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2] , where [.] denotes t...

    Text Solution

    |

  14. Let f(x)=e^{e^((|x|)sinx})a n dg(x)=e^{e^((|x|)sinx}),x in R , where ...

    Text Solution

    |

  15. The number of solutions of the equation [y+[y]]=2 cosx, where y=(1)...

    Text Solution

    |

  16. The function f(x)=sin(log(x+sqrt(1+x^2))) is (a) even function (b) odd...

    Text Solution

    |

  17. If f(x)=x^m n ,n in N , is an even function, then m is even integer ...

    Text Solution

    |

  18. If f(x)={x^2 sin((pi x)/2), |x|<1; x|x|, |x|>=1 then f(x) is

    Text Solution

    |

  19. If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetrical ...

    Text Solution

    |

  20. If f: Rvec is an invertible function such that f(x)a n df^(-1)(x) are ...

    Text Solution

    |