Home
Class 12
MATHS
If f(x)=log[(1+x)/(1-x)], then prove tha...

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

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

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

If f(x)=2^(x) , then prove that f(x +1) = 4f( x - 1).

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

Find the domain of definition of f(x)=log_e.(1-x)/(1+x). Further show that, f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2)),x_1,x_2 in (-1,1)

If f(x) = log_e ((1-x)/(1+x)) , then f' (0) is

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Let f(x)={1+|x|,x<-1 [x],xgeq-1 , where [.] denotes the greatest integ...

    Text Solution

    |

  2. Let f:(-pi/2,pi/2)vecR be given by f(x)=(log(sec"x"+tan"x"))^3 then f(...

    Text Solution

    |

  3. If f(x)=log[(1+x)/(1-x)], then prove that f[(2x)/(1+x^2)]=2f(x)dot

    Text Solution

    |

  4. If f: RrarrR and g:RrarrR are two given functions, then prove that 2...

    Text Solution

    |

  5. Find the range of f(x)(x^2-x+1)/(x^2+x+1)

    Text Solution

    |

  6. Find the range of the function f(x)=cot^(-1)(log)(0. 5)(x^4-2x^2+3)

    Text Solution

    |

  7. Find the domain and range of f(x)=sqrt(3-2x-x^2)

    Text Solution

    |

  8. If f(x)=sinx+cosx and g(x)=x^2-1, then g(f (x)) is invertible in the ...

    Text Solution

    |

  9. Find the domain of f(x)=sqrt(((1-5^x)/(7^(-x)-7)))

    Text Solution

    |

  10. If f is the greatest integer function and g is the modulus function, t...

    Text Solution

    |

  11. If the functions f(x)a n dg(x) are defined on R rarr R such that f(x)=...

    Text Solution

    |

  12. Suppose that g(x)=1+sqrt(x) and f(g(x))=3+2sqrt(x)+xdot Then find the ...

    Text Solution

    |

  13. Let f: R->R \ w h e r e \ f(x)=(x^2+4x+7)/(x^2+x+1) . Is f(x) \ on e \...

    Text Solution

    |

  14. X and Y are two sets and f: X->Y If {f(c)=y; c subX, y subY} and {f^(-...

    Text Solution

    |

  15. The function f(x) is defined in [0,1] . Find the domain of f(t a nx)do...

    Text Solution

    |

  16. Find the equivalent definition of f(x)=max{x^2,(1-x)^2,2x(1-x)}where ...

    Text Solution

    |

  17. If y=f(x)=((x+2))/((x-1)),t h e n (a) x=f(y) (b) f(1)=3 (c)y increa...

    Text Solution

    |

  18. Find the period of (|sin4x|+|cos4x|)/(|sin4x-cos4 x|+|sin4x+cos4x|)

    Text Solution

    |

  19. Consider the function: f(x)=m a xdot{1,|x-1|, min {4,|3x-1|}}AAx in ...

    Text Solution

    |

  20. Let g(x) be a function defined on[-1,1]dot If the area of the equila...

    Text Solution

    |