Home
Class 12
MATHS
Find the domain and range function f(x...

Find the domain and range function `f(x) =(x^(2)-3x+2)/(x^(2)-4x+3)`.

Text Solution

Verified by Experts

`y=f(x)=((x-1)(x-2))/((x-3)(x-1))=(x-2)/(x-3), x ne 1,3`
Domain of function `=R-{1,3}`
Now `yx-3y=x-2`
` :. x= (3y-2)/(y-1)`
Clearly `y ne 1`.
Also, when ` x=1, y=1//2`
Therefore, range of function is ` R-{(1)/(2),1}`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

What is the domain and range of the function f(x)=(x^(2)-3x+2)/(x^(2)+x-6) . Find the limit of f(x) as x approaches 2.

Find the domain and range of the function f(x)=2-|x-5|

Find the domain and range of the function f(x)=x/(x^2-5x+4)

Find the domain and range of the function f(x)=(x)/(x^2-5x+4)

Find the domain of the function f(x) =(x^(2)+2x+1)/(x^(2)-8x+12)

Find the domain of the function f(x)=(x^(2)+3x+5)/(x^(2)-5x+4)

Find the domain and range of the function f(x)=(x^2)/(1+x^2) . Is the function one-to-one?

Find the domain and range of f(x)=sqrt(4-16x^(2)) .

Find the domain and range of the function f(x)="sin"^(-1)(x^(2))/(2)

Find the domain and range of the real function f(x)=1/((1-x^2))

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Write explicit functions of y defined by the following equations and a...

    Text Solution

    |

  2. Find the domain and range of the following functions. (i) f(x)=sqrt...

    Text Solution

    |

  3. Find the domain and range function f(x) =(x^(2)-3x+2)/(x^(2)-4x+3).

    Text Solution

    |

  4. Find the values of x for which the following functions are identical....

    Text Solution

    |

  5. ABCD is a square of side l. A line parallel to the diagonal BD at a di...

    Text Solution

    |

  6. The relation f is defined by f(x) ={(3x+2", "0le x le2),(x^(3)", ...

    Text Solution

    |

  7. If f: [-3,4] to R,f(x)=2x, " and " g :[-2, 6] to R,g(x) =x^(2). Then f...

    Text Solution

    |

  8. If f(x) ={(x^(3)", " x lt1),(2x-1", " x ge 1):} " and " g(x)={(...

    Text Solution

    |

  9. Check the nature of the following function. (i) f(x)=sin x, x in R...

    Text Solution

    |

  10. Check the nature of the function f(x)=x^(3)+x+1, x in R using analyt...

    Text Solution

    |

  11. Let f: R->R \ w h e r e \ f(x)=(x^2+4x+7)/(x^2+x+1) . Is f(x) \ on e \...

    Text Solution

    |

  12. Let f:R to R where f(x) =sin x. Show that f is into. Also find the co...

    Text Solution

    |

  13. Let f: N->Z be a function defined as f(x)=x-1000. Show that f is an in...

    Text Solution

    |

  14. If the function f: RvecA given by f(x)=(x^2)/(x^2+1) is surjection, th...

    Text Solution

    |

  15. Let A={x:-1 le x le 1}=B be a function f: A to B. Then find the nature...

    Text Solution

    |

  16. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

    Text Solution

    |

  17. If f:[0,oo) to [0,1), " and " f(x)=(x)/(1+x) then check the nature o...

    Text Solution

    |

  18. If the functions f(x) and g(x) are defined on R -> R such that f(x)=...

    Text Solution

    |

  19. Show that f: R->R defined by f(x)=(x-1)(x-2)(x-3) is surjective but no...

    Text Solution

    |

  20. Let f : R to R be a function such that f(x)=x^3+x^2+3x+sinx . Then

    Text Solution

    |