Home
Class 12
MATHS
If f(x)={x ,xi sr a t ion a l1-x ,xi si ...

If `f(x)={x ,xi sr a t ion a l1-x ,xi si r r a t ion a l ,t h e nf(f(x))` is `xAAx in R` (b) `{x , xi si r r a t ion a l1-x ,xi sr a t ion a l` `{x ,xi sr a t ion a l1-x ,xi si r r a t ion a l` (d) none of these

A

`x AA x in R`

B

`f(x)={(x",",x" is irrational"),(1-x",",x" is rational"):}`

C

`f(x)={(x",",x" is rational"),(1-x",",x" is irrational"):}`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`f(f(x))={(f(x)",",f(x)" is rational"),(1-f(x)",",f(x)" is irrational"):}`
`f(x)={(x",",x" is rational"),(1-(1-x)=x",",x" is irrational"):}`.
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

Discuss the continuity of f(x)={x^2,xi sr a t ion a l-x^2,xi si r r a t ion a ldot

Find the value of x where f(x)={x ,ifxi sr a t ion a l1-x ,ifxi si r r a t ion a li scon t inuou sdot

If the functions f(x)a n dg(x) are defined on R rarr R such that f(x)={0, x in r a t ion a l x ,x in i r r a t ion a l a n dg(x)={O , x in i r r a t ion a l x ,x in r a t ion a l then (f-g)(x)i s (a)one-one and onto (b)neither one-one nor onto (c)one-one but not onto (d)onto but not one-one

Discuss the continuity of the following function : f(x)={1,ifxi sr a t ion a l0,ifxi si r r a t ion a l

Find the value of x where f(x)={x ,\ if\ x\ r a t ion a l1-x ,\ if\ x\ i s\ irrational\ is\ contiuous.

Statement 1: If f(x)={x ,\ if\ x\ i s\ irr a t ion a l1-x ,\ if\ x\ i s\ r a t ion a l\ ,\ t h e n(lim)_(x->1//2)f(x) does not exist. Statement 2: x->1/2 can be rational or irrational value. Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true; Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

Discuss the continuity of the following function f(x)={1,\ if\ x\ i s\ r a t ion a l , 0\ if\ x\ i s\ irrational

Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly two points of continuity then the value of b are (0,3] b. [0,1] c. (0,2] d.varphi

Let f(x)=("lim")_(nvecoo){("lim")_(nvecoo)cos^(2m)(n !pix)}, where x in Rdot Then prove that f(x)={1,ifxi sr a t ion a l0,ifxi si r r a t ion a l

For x >0,l e th(x)={1/q ,ifx=p/q0,ifxi si r r a t ion a l where p ,q >0 are relatively prime integers. Then prove that f(x) is continuous for all irrational values of xdot

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. If f(x)={(x^(2)",","for "x ge0),(x",","for "x lt 0):}, then fof(x) is...

    Text Solution

    |

  2. Let f(x)=sinx and g(x)=(log)e|x|dot If the ranges of the composition f...

    Text Solution

    |

  3. If f(x)={x ,xi sr a t ion a l1-x ,xi si r r a t ion a l ,t h e nf(f(x)...

    Text Solution

    |

  4. If f and g are one-one functions, then

    Text Solution

    |

  5. The domain of f(x)i s(0,1)dot Then the domain of (f(e^x)+f(1n|x|) is

    Text Solution

    |

  6. Let h(x)=|k x+5|,the domain of f(x) be [-5,7], the domain of f(h(xx)) ...

    Text Solution

    |

  7. If f(x)=sinx+cosx and g(x)=x^2-1, then g(f (x)) is invertible in the ...

    Text Solution

    |

  8. If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then ...

    Text Solution

    |

  9. Let f(x)=(x+1)^2-1, xgeq-1. Then the set {x :f(x)=f^(-1)(x)} is {0,1,(...

    Text Solution

    |

  10. if f:[1,oo)->[2,oo) is given by f(x)=x+1/x then f^-1(x) equals to

    Text Solution

    |

  11. Suppose f(x)=(x+1)^2forxgeq-1. If g(x) is the function whose graph is ...

    Text Solution

    |

  12. Let f:[-pi/3,(2pi)/3]vec[0,4] be a function defined as f(x)=sqrt(3)sin...

    Text Solution

    |

  13. Which of the following functions is the inverse of itself? f(x)=(1-x)/...

    Text Solution

    |

  14. If g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2, then which is not a possible ...

    Text Solution

    |

  15. Let f: Xvecyf(x)=s inx+cosx+2sqrt(2) be invertible. Then which XvecY i...

    Text Solution

    |

  16. If f(x) is an invertible function and g(x)=2f(x)+5, then the value of ...

    Text Solution

    |

  17. Let f(x)=[x] +sqrt({x}), where [.] denotes the integral part of x and...

    Text Solution

    |

  18. If f is a function such that f(0)=2,f(1)=3,a n df(x+2)=2f(x)-f(x+1) fo...

    Text Solution

    |

  19. A function f(x) satisfies the functional equation x^2f(x)+f(1-x)=2x-x^...

    Text Solution

    |

  20. If f(x) is a polynomial satisfying f(x)f(1/x)=f(x)+f(1/x)a n df(3)=28 ...

    Text Solution

    |