Home
Class 11
MATHS
If f is a real function defined by f(x)=...

If `f` is a real function defined by `f(x)=(x-1)/(x+1)`, then prove that `f(2 x)=(3f(x)+1)/(f(x)+3)`.

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|89 Videos

  • SEQUENCES AND SERIES

    V PUBLICATION|Exercise QUESTIONBANK|140 Videos

Similar Questions

Explore conceptually related problems

If f:RtoR is a function defined by f(x)=3x-2 Show that f is one-one.

If f(x) = log [(1+x)/(1-x)] , the prove that f[(2x)/(1+x^2)] =2f(x)

A fuction f:RrarrR defined by f(x)=(2x-3)/7 . Find f^-1

Consider the real function f(x)=(x+2)/(x-2) Prove that f(x)f(-x)+f(0)=0

The function f is defined by f(x)={(2-x,,x, ,0):} Draw the graph of Find f(x)

Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continuous at x=2?

Consider the function f:R rarr R defined by f(x)=|x-1| . Draw the graph of f(x).

Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continuous at x=1?

Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continuous at x=0

A fuction f:RrarrR defined by f(x)=(2x-3)/7 ii.Prove that f is invertible.

V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTIONBANK
  1. Let R be the relation on the set Z of all integers defined by R={(x, y...

    Text Solution

    |

  2. Let f be defined by f(x)=x-4 and g be defined by g(x)=(x^2-16)/(x+4), ...

    Text Solution

    |

  3. If f is a real function defined by f(x)=(x-1)/(x+1), then prove that f...

    Text Solution

    |

  4. Find the domain and range of the following functions: i)f(x)=1/(sqrt(x...

    Text Solution

    |

  5. Let f and g be two real functions defined by f(x)=1/(x+4) and g(x)=(x+...

    Text Solution

    |

  6. Which of the following relations are functions? Give reasons. If it is...

    Text Solution

    |

  7. If f(x)=x^2+x-1 and g(x)=4 x-7. be real functions then find: i) (f+g)...

    Text Solution

    |

  8. Let f and g be real functions defined by f(x)=sqrt(x+4), x ge-4 and g(...

    Text Solution

    |

  9. If af(x)+bf (1/x)=1/x-5 for x ne 0, where a ne b. Find f(x)

    Text Solution

    |

  10. If A={3,4,6} , B={1,3} and C={1,2,6}, then find (i) A xx(B nn C) (...

    Text Solution

    |

  11. Let A and B are two sets such that n (A) = 3 and n (B) = 2. If (x,1),...

    Text Solution

    |

  12. Let A be a non - empty set such that A xx B=A xx C show that B=C

    Text Solution

    |

  13. Let A subset B, C subset D, then prove that A xx C subset B xx D

    Text Solution

    |

  14. Let R be the relation on Z defined by R={(a, b), a, b in Z, a^2=b^2} F...

    Text Solution

    |

  15. Let R be the relation on Z defined by R = { ( a,b): a,b in Z, a - b i...

    Text Solution

    |

  16. If f :R rarr R is defined by f(x)=x^2-3 x+2, find f(f(x)). Also evalua...

    Text Solution

    |

  17. If f(x)=x+1/x show that (f(x))^3=f(x^3)+3 f(x)

    Text Solution

    |

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

    Text Solution

    |

  19. Draw the graph of the real function y=x^2+2 x+3

    Text Solution

    |

  20. Draw the graph of the real function y={[ x, if x le 0], [ x^2, if...

    Text Solution

    |