Home
Class 12
MATHS
If f(x)=log((1+x)/(1-x)), "then f "((2x)...

If `f(x)=log((1+x)/(1-x))`, `"then f "((2x)/(1+x^(2)))` is equal to

A

`(f(x))^(2)`

B

1

C

`2f(x)`

D

`f((1-x)/(1+x))`

Text Solution

Verified by Experts

The correct Answer is:
C
Given that `f(x)=log((1+x)/(1-x))`
So, `f((2x)/(1+x^(2)))=log(1+(2x)/((1+x^(2))/(1-(2x)/(1+x^(2)))))`
`=log((1+x^(2)+2x)/(1+x^(2)-2x))=log(((1+x)^(2))/((1-x))^(2))`
`=log((1+x)/(1-x))^(2)=2log((1+x)/(1-x))`
`=2f(x)" "["sincef(x)=log((1+x)/(1-x))]`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 Videos

Similar Questions

Explore conceptually related problems

If f(x)=log((1+x)/(1-x)) and then f((2x)/(1+x^(2))) is equal to {f(x)}^(2) (b) {f(x)}^(3)(c)2f(x)(d)3f(x)

If f(x) = log_(e) ((1-x)/(1+x)) , then f((2x)/(1 + x^(2))) is equal to :

if f(x)=log_(2)((1-x)/(1+x)) then f((2x)/(1+x^(2))) is equal to (A) f(x) (B) 2f(x) (C) -2f(x) (D) (f(x))^(2)

If f(x)=log_(e)((1-x)/(1+x)),|x|<1, then f((2x)/(1+x^(2))) is equal to:

If f(x)=log_(e)((1-x)/(1+x)),|x| lt 1, " then " f((2x)/(1+x^(2))) is equal to

If f(x)=log((1+x)/(1-x)) show that f((2x)/(1+x^(2)))=2(f(x))

If f(x)=log((1-x)/(1+x)),-1ltxlt1 , then f(-x)=f(x) .

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. If f(x)=[{:(mx+1,if x le (pi)/(2)),(sinx+n,ifxgt(pi)/(2)):} is contin...

    Text Solution

    |

  2. The above curve shows the graph of a^(x) under which one of the follow...

    Text Solution

    |

  3. If f(x)=log((1+x)/(1-x)), "then f "((2x)/(1+x^(2))) is equal to

    Text Solution

    |

  4. If f(x)=(x+1)^(cotx) is continuous at x=0, then what is f(0) equal to?

    Text Solution

    |

  5. What is the value of lim(xtooo) ((x-2)/(x+2))^(x+2) = ?

    Text Solution

    |

  6. If the derivative of the function f(x) ={ax^2+b , x lt -1 and bx^2 ...

    Text Solution

    |

  7. If f(x) is differentiable everywhere, then which one of the following ...

    Text Solution

    |

  8. Consider the cubic equation x^3 + ax^2 + bx + c = 0, where a, b, c are...

    Text Solution

    |

  9. If (x-a)/(b+c)+(x-b)/(c+a)+(x-c)/(a+b)=3 then value of x is

    Text Solution

    |

  10. If -x^(2)+3x+4gt0, then which one of the following is correct?

    Text Solution

    |

  11. Given f(x)=x+(1)/(x), then what is f^(2)(x) equal ot ?

    Text Solution

    |

  12. If f(x)={{:(1,x" is a rational number"),(0",","x is an irrational numb...

    Text Solution

    |

  13. A function f is defined as follows f(x)=x^(p)cos((1)/(x)),xne0 f(0...

    Text Solution

    |

  14. What is the value of lim(xto0) (sinx)/(x)?

    Text Solution

    |

  15. What is lim(xto0)(a^(x)-b^(x))/(x)?

    Text Solution

    |

  16. Let f(x)={{:(3x-4",",0lexle2),(2x+l",",2ltxle9):} If is continuous a...

    Text Solution

    |

  17. If f(x)=xandg(x)=|x|, then what is (f+g)(x) equal to ?

    Text Solution

    |

  18. If g(x)=sinx,x""inRandf(x)=(1)/(sinx),x"in(0,(pi)/(2)) what is (gof)(x...

    Text Solution

    |

  19. Let f:RtoR be defined as f(x)=sin(|x|) Which one of the following is...

    Text Solution

    |

  20. What is the inverse of the function y=5^(logx)?

    Text Solution

    |