Home
Class 9
MATHS
If f(x) = (x-1)/(x+1), then prove that (...

If `f(x) = (x-1)/(x+1)`, then prove that `(f(x)-f(y))/(1+f(x)f(y))=(x-y)/(1+xy)`.

Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.3|36 Videos

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.4|52 Videos

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.1|57 Videos

  • LOGARITHM

    CALCUTTA BOOK HOUSE|Exercise Exercise - 7 (Long-answer type questions)|49 Videos

  • PROBABILITY

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 2|16 Videos

Similar Questions

Explore conceptually related problems

If y = f(x) = (x+2)/(x-1) then

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

If f(x)=(1-x)/(1+x), prove that f[f{f(1/x)}]=-f(x)

If f(x)=5^x , then prove : f(x+y)=f(x).f(y)

If 2f(x-1)-f((1-x)/x)=x , then prove that 3f(x)=2(x+1)+1/(x+1) .

If f(x)=(1-x)/(1+x), prove that f{f((1)/(x))}=1/x[x ne0]

If f(x) = 1/(1-x) , then f[f{f(x)}] is

If , f(x)="log"((1+x)/(1-x)) ,show that f(x)+f(y)=f((x+y)/(1+xy))

If f(x + y) = f(x) +f(y), then the value of f(0)

If f(x)=cos(logx) ,show that f(x)f(y)-1/2 [ f (x/y) + f(xy) ]=0

CALCUTTA BOOK HOUSE-POLYNOMIALS-EXERCISE-1.2
  1. If f(x)=(1-x)/(1+x), then prove that f(x)+f(1/x)=0.

    Text Solution

    |

  2. Find the zeroes of the polynomial p(x)=x^(2)-(a+1/a)x+1.

    Text Solution

    |

  3. If f(x)=log(2)xandg(x)=x^(2) then find f(g(2)).

    Text Solution

    |

  4. If f(x)=x^(2)andg(x)=sqrtx, then prove that g(f(4)) = 4.

    Text Solution

    |

  5. If f(x)=4^(x), then prove that (f(x+1))/(f(x-1))=16.

    Text Solution

    |

  6. The polynomial f(x) is defined by f(x)={{:("0 when x is an integer ,...

    Text Solution

    |

  7. If the polynomial f(x) be defined by f(x) = {{:(2x^(2)-3 " when " xl...

    Text Solution

    |

  8. If f(x) = ax + b, f(0) = 2 and f(4) = 10, then find the values of a an...

    Text Solution

    |

  9. If 2f(x) + 3f(-x) = 15 - 4x, then prove that f(x) = 3 + 4x.

    Text Solution

    |

  10. If f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the va...

    Text Solution

    |

  11. If f(x)=ax^(2)+bx+c and f(x - 1) = f(x) + 2x + 1. then find the values...

    Text Solution

    |

  12. If f(x)=1/(4x^(2)), then proved that (f(x-h)-f(x+h))/h=x/((x^(2)-h^(2)...

    Text Solution

    |

  13. If y=f(x)=(2x+3)/(5x-a), then determine the value of a so that x = f(y...

    Text Solution

    |

  14. If f(x) = (x-1)/(x+1), then prove that (f(x)-f(y))/(1+f(x)f(y))=(x-y)/...

    Text Solution

    |

  15. If 2f(x-1)-f((1-x)/x)=x, then prove that 3f(x)=2(x+1)+1/(x+1).

    Text Solution

    |

  16. If xgt0, then prove that the value of the polynomial (2x+2^(-x)-2) is ...

    Text Solution

    |

  17. If f(x)=(x-a)/x+x/(x-b), then find f((a+b)/2).

    Text Solution

    |

  18. If 3f(x)-f(1/x)=log(e)x^(4)(xgt0), then prove that f(e^(x))=x.

    Text Solution

    |

  19. If f(x)=x^(9)-2x^(8)-2x^(6)+4x^(5)+x^(4)-2x^(3)+x-1, then find the val...

    Text Solution

    |

  20. If f(x)=(a-x^(n))^(1/n),agt0 and n is a positive integer, then prove t...

    Text Solution

    |