Home
Class 11
MATHS
If f: R->R : x!=0,\ -4lt=xlt=4 and f: A-...

If `f: R->R : x!=0,\ -4lt=xlt=4` and `f: A->A` be defined by `f(x)=(|x|)/x` for `x in A` . Then `A` is `{1,-1}` b. `{x :0lt=xlt=4}` c. `{1}` d. `{x :-4lt=xlt=0}`

Text Solution

Verified by Experts

Given that,
`f(x)=|x|/x`
If `x lt 0`
`|x|=x`
...
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    RD SHARMA|Exercise Solved Examples And Exercises|97 Videos
  • GEOMETRIC PROGRESSIONS

    RD SHARMA|Exercise Solved Examples And Exercises|255 Videos

Similar Questions

Explore conceptually related problems

Let A={x in R :-4lt=xlt=4 and x!=0} and f: A->R be defined by f(x)=(|x|)/x . Write the range of fdot

Let f: (0,1) to R be defined by f(x)=(b-x)/(1-bx) where b is a constant such that 0 lt b lt 1 Then:

If f: R to R be defined by f(x)={(2x:xgt3),(x^(2):1lt x le 3),(3x:x le 1):} Then, f(-1)+f(2)+f(4) is

Let A={x in R :0lt=xlt=1}dot If f: AvecA is defined by f(x)={x ,ifx Q1-x ,ifx Q then prove that fof(x)=x for all x in Adot

If f'(x)=(1)/(1+x^(2)) for all x and f(0)=0 , show that 0.4 lt f (2) lt2

If f(x)=[(x,xlt1),(x^(2),1lexle4),(8sqrt(x),xgt4):} the find f^(-1)(x) .

A function f is defined by f(x)=\ int_0^picostcos(x-t)dt ,\ 0lt=xlt=2pi then find its minimum value.

The relation f is defined by f(x)={x^2,""0lt=xlt=3 3x ,""""3lt=xlt=10 The relating g is defined by g(x)={x^2,""0lt=xlt=3 3x ,""""2lt=xlt=10 Show that f is a function and g is not a function.

RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. Let A and B be any two sets such that n(B)=P, n(A)=q then the total nu...

    Text Solution

    |

  2. Find the values of x for which the functions f(x)=3x^2-1 and g(x)=3+x ...

    Text Solution

    |

  3. If f(x)="cos"((log)e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value ...

    Text Solution

    |

  4. Let f(x)=|x-1|dot Then (a)f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c)f(...

    Text Solution

    |

  5. If A={1,2,3},\ B={x , y} , then the number of functions that can be de...

    Text Solution

    |

  6. If x!=1\ a n d\ f(x)=(x+1)/(x-1) is a real function, then f(f(f(2))) ...

    Text Solution

    |

  7. If f: R->R : x!=0,\ -4lt=xlt=4 and f: A->A be defined by f(x)=(|x|)/x ...

    Text Solution

    |

  8. If f: RrarrR and g: RrarrR are defined by f(x)=2x+3a n dg(x)=x^2+7, th...

    Text Solution

    |

  9. If f: [-2, 2] -> R is defined by f(x)={-1,for -2<=x<=0 , then x...

    Text Solution

    |

  10. If f(x)=64x^3+1/x^3 and alpha,beta are the roots of 4x+1/x=3. Then,f(a...

    Text Solution

    |

  11. The domain of the function f(x)=sqrt(2-2x-x^2) is [-sqrt(3),\ sqrt(3)...

    Text Solution

    |

  12. The domain of the function f(x)=sqrt[((x+1)(x-3))/(x-2)] is [-1,2)uu[3...

    Text Solution

    |

  13. The domain of the function f(x)=sqrt(((x+1)(x-3))/(x-2)) is [-1,2)uu[3...

    Text Solution

    |

  14. The domain of definition of the function f(x)=sqrt(x-1)+sqrt(3-x) is [...

    Text Solution

    |

  15. The domain of definition of the function f(x)=sqrt((x-2)/(x+2))+sqrt((...

    Text Solution

    |

  16. The domain of definition of the function f(x)="log"|x| is R b. (-oo...

    Text Solution

    |

  17. The domain of definition of f(x)=sqrt[x-3-2sqrt(x-4)]-sqrt[x-3+2sqrt(x...

    Text Solution

    |

  18. The domain of the function f(x)=sqrt(5|x|-x^2-6) is (a) (-3,\ -2)uu(...

    Text Solution

    |

  19. The range of the function f(x)=(x+2)/(|x+2|),\ x!=-2

    Text Solution

    |

  20. The range of the function f(x)=x/(|x|) is R-{0} b. R-{-1,1} c. {-1,1}...

    Text Solution

    |