Home
Class 12
MATHS
If f(x)=(x-1)/(x+1),x!=-1, then show tha...

If `f(x)=(x-1)/(x+1),x!=-1,` then show that `f(f(x))=-1/x` provided that `x != 0,-1

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)=(x-1)/(x+1),x!=-1, . then show that f(f(x))=-1/x , prove that x!=0 .

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) =(x-1)/(x+1), then prove that f{f(x)}=-1/x.

If f(x)=(4^(x))/(4^(x)+2) , then show that f(x)+f(1-x)=1

If f(x)=(x+1)/(x-1) , show that f{f(x)}=xdot

If f(x)=(x-1)/(x+1) , then show that f(1/x)=-f(x) (ii) f(-1/x)=-1/(f(x))

If f(x)=(x-1)/(x+1) , then show that f(1/x)=-f(x) (ii) f(-1/x)=1/(f(x))

If y = f(x) = (x+2)/(x-1) , x ne1 , then show that x = f(y) .

If f(x)=x^3-1/(x^3) , show that f(x)+f(1/x)=0.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A}x :-1lt=xlt=1}a n df: Avec A such that f(x)=x|x|, then f is (a) ...

    Text Solution

    |

  2. If the function f:[1,oo)rarr[1,oo) is defined by f(x)=2^(x(x-1)),t h e...

    Text Solution

    |

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

    Text Solution

    |

  4. Let f be a real function defined by f(x)=sqrt(x-1.) Find (fofof)(x)dot...

    Text Solution

    |

  5. Let f: R-> R be the function defined by f(x)=4x−3 for all x in R. Then...

    Text Solution

    |

  6. Find whether f: R->R given by f(x)=x^3+2 for all x in R .

    Text Solution

    |

  7. Find whether f: Z->Z given by f(x)=x^2+1 for all x in Z

    Text Solution

    |

  8. Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , i...

    Text Solution

    |

  9. Discuss the surjectivity of f: R->R given by f(x)=x^3+2 for all x i...

    Text Solution

    |

  10. Discuss the surjectivity of f: R->R given by f(x)=x^2+2 for all x i...

    Text Solution

    |

  11. Discuss the surjectivity of f: Z->Z given by f(x)=3x+2 for all x in...

    Text Solution

    |

  12. Show that the function f: N->N given by f(1)=f(2)=1 and f(x)=x-1 for e...

    Text Solution

    |

  13. Show that the Signum function f:R->R, given by f(x)={(1,xgt0),(0,x=0),...

    Text Solution

    |

  14. Prove that the function f: Q->Q given by f(x)=2x-3 for all x in Q ...

    Text Solution

    |

  15. Show that the function f: R->R defined by f(x)=3x^3+5 for all x in R ...

    Text Solution

    |

  16. Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(...

    Text Solution

    |

  17. Let A be the set of all 50 students of class X I I in a central scho...

    Text Solution

    |

  18. Show that the function f: N->N , given by f(x)=2x , is one-one but not...

    Text Solution

    |

  19. Prove that f: R->R , given by f(x)=2x , is one-one and onto.

    Text Solution

    |

  20. Show that the function f : R ->R, defined as f(x)=x^2, is neither one-...

    Text Solution

    |