Home
Class 12
MATHS
If f(x)=(4x+3)/(6x-4),\ x\ !=2/3, show t...

If `f(x)=(4x+3)/(6x-4),\ x\ !=2/3,` show that `fof(x)=x` for all `x!=2/3dot` What is the inverse of `f?`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

Similar Questions

Explore conceptually related problems

If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

If f(x)=x^(3)-4 , then the inverse of f=

f(x)=3x+2 . Is g(x)=(x-2)/(3) the inverse of f?

If f(x)=1/(2x+1),\ x!=-1/2,\ then show that f(f(x))=(2x+1)/(2x+3) , provided that x!=-3/2dot

If f(x)=1/(2x+1),\ x!=-1/2,\ then show that f(f(x))=(2x+1)/(2x+3) , provided that x!=-3/2dot

If f(x)=3x^(2)-2x+4,f(-2)=

Consider f : R->{-4/3}->R-{4/3} given by f(x) = (4x+3)/(3x+4) . Show that f is bijective. Find the inverse of f and hence find f^(-1)(0) and x such that f^-1(x) = 2 .

Given that f(x) = 4 x ^2 and g (x) =3-(x)/(2) , what is the value of f(g(4)) ?

If f(x) =1- x, x in [-3,3] , then the domain of fof (x) is

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Consider f: R->Rgiven by f(x) = 4x + 3. Show that f is invertible. Fin...

    Text Solution

    |

  2. Consider f\ : R+vec[4,oo) given by f(x)=x^2+4 . Show that f is inve...

    Text Solution

    |

  3. If f(x)=(4x+3)/(6x-4),\ x\ !=2/3, show that fof(x)=x for all x!=2/3dot...

    Text Solution

    |

  4. Consider f: R+->[-5,oo)given by f(x)=9x^2+6x-5. Show that f is inverti...

    Text Solution

    |

  5. If f: R->R be defined by f(x)=x^3-3 , then prove that f^(-1) exists an...

    Text Solution

    |

  6. A function f: R->R is defined as f(x)=x^3+4 . Is it a bijection or not...

    Text Solution

    |

  7. If f: Q->Q ,\ \ g: Q->Q are two functions defined by f(x)=2x and g(x)=...

    Text Solution

    |

  8. Let A=R-{3}a n dB=R-{1}dot Consider the function f: Avec defined by f(...

    Text Solution

    |

  9. Consider f:R+->[-9,oo[ given by f(x)=5x^2+6x-9. Prove that f is invert...

    Text Solution

    |

  10. Let f: Nvec be a function defined as f(x)=9x^2+6x-5. Show that f: Nvec...

    Text Solution

    |

  11. If f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is inve...

    Text Solution

    |

  12. If f: R->(0,\ 2) defined by f(x)=(e^x-e^(-x))/(e^x+e^(-x))+1 is invert...

    Text Solution

    |

  13. Let f:[-1,oo]vec[-1,) is given by f(x)=(x+1)^2-1,xgeq-1. Show that f i...

    Text Solution

    |

  14. Let A={x in R|-1lt=xlt=1} and let f: A->A ,\ g: A->A be two functions...

    Text Solution

    |

  15. Let f be a function from R to R such that f(x)=cos(x+2) . Is f inverti...

    Text Solution

    |

  16. If A={1,\ 2,\ 3,\ 4} and B={a ,\ b ,\ c ,\ d} . Define any four bij...

    Text Solution

    |

  17. Let A and B be two sets each with a finite number of elements. Assume ...

    Text Solution

    |

  18. If f: AvecA ,g: Avec are two bijections, then prove that fog is an inj...

    Text Solution

    |

  19. If f: A->A ,\ \ g: A->A are two bijections, then prove that fog is an ...

    Text Solution

    |

  20. Which one of the following graphs represent a function? (FIGURE)

    Text Solution

    |