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(2x)=(3f(x)+1)/(f(x)+3)`

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise Exercise-2(a)|25 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise Exercise 2(b)|14 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise Frequently Asked Questions|17 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

Let (x) is a real function, defines as f(x) =(x-1)/(x+1), then prove that f(2x)=(3f(x)+1)/(f(x)+3).

If f(x)=x+(1)/(x) , then prove that : {f(x)}^(3)=f(x^(3))+3*f((1)/(x))

If f(x)=(1+x)/(1-x), show that: f(2x)=(3f(x)-1)/(3-f(x)) .

If a function f(x) is defined as f(x)={-x,x 1 then

If f(x) is a real-valued function defined as f(x)=In (1-sinx), then the graph of f(x) is

If is a real valued function defined by f(x)=x^(2)+4x+3, then find f'(1) and f'(3)

If f(x) is a real valued function defined as f(x)=In(1-sin x) then graph of f(x) is

If f(x),=x+(1)/(x), prove that [f(x)]^(3),=f(x^(3))+3f((1)/(x))dots

If 'f' is an invertible function,defined as f(x)=(3x-4)/(5), write f^(-1)(x)

Let the function f be defined by f(x)=((2x+1)/(1-3x)) then f^(-1)(x) is

MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Illustrative Example
  1. Let A = {1, 2, 3}, B = {4, 5, 6, 7}and let f = {(1, 4), (2, 5), (3, 6)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. If f(x)=1/(2x+1),\ x!=-1/2,\ then show that f(f(x))=(2x+1)/(2x+3) , p...

    Text Solution

    |

  5. If f(x)=loge((1-x)/(1+x)); prove that f(a)+f(b)=f((a+b)/(1+a b))

    Text Solution

    |

  6. माना f:R rarr R एक फलन इस प्रकार परिभाषित है, कि f(x)={:{(3x-1, " ...

    Text Solution

    |

  7. For the relation y= + sqrtx, say whether it is a function or not. If i...

    Text Solution

    |

  8. Find the domain and range of the following functions: (i) f(x) = sqr...

    Text Solution

    |

  9. The domain of the function f(x)=1/(sqrt([x]^2-2[x]-8)) is, where [*] d...

    Text Solution

    |

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

    Text Solution

    |

  11. Find the range of the following function: f(x) = (1)/((2x-3) (x+1))

    Text Solution

    |

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

    Text Solution

    |

  13. Which of the following functions are odd or even or neither: (i) f(x...

    Text Solution

    |

  14. The period of x-[x] where [x] represents the integral part of x is

    Text Solution

    |

  15. Solve: [2x-3]=5

    Text Solution

    |

  16. Let f and g be two functions defined by: f(x) = sqrt(x-1) and g(x) = s...

    Text Solution

    |

  17. The domain of the function f(x)=(sin^(-1)x)/([x]) is (where is greates...

    Text Solution

    |

  18. Define the function f : R -> R by y = f(x) = x^2 , x in R . ...

    Text Solution

    |

  19. Draw the graph of the function: f: R rarr R defined by f(x) = x^(3), x...

    Text Solution

    |

  20. Let R be the set of real numbers. Define a real function f: R rarr R "...

    Text Solution

    |