Home
Class 12
MATHS
Let f: (e, oo) -> R be defined by f(x) =...

Let `f: (e, oo) -> R` be defined by `f(x) =ln(ln(In x))`, then

A

`f` is one one but not onto

B

`f` is onto but not one-one

C

`f` is one-one and onto

D

`f` is neither one-one nor onto

Text Solution

Verified by Experts

The correct Answer is:
C
NA
Promotional Banner

Topper's Solved these Questions

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise MATCH THE COLUMN|2 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise INTEGER_TYPE|21 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise SUBJECTIVE_TYPE|179 Videos

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

  • SEQUENCE & SERIES

    RESONANCE ENGLISH|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 Videos

Similar Questions

Explore conceptually related problems

Let f:[4,oo)to[4,oo) be defined by f(x)=5^(x^((x-4))) .Then f^(-1)(x) is

Let f:R to R be defined by f(x) =e^(x)-e^(-x). Prove that f(x) is invertible. Also find the inverse function.

Let f:Rto R be a functino defined by f (x) = e ^(x) -e ^(-x), then f^(-1)(x)=

Let a function f:R^(+) to R is defined as f(x)="log"_(e)x, then find each of the following: (i) Range of f (ii) f(x)=-2 (iii) Is f(xy)=f(x)+f(y) true ?

Let f : R ^(+) to R defined as f (x)= e ^(x) + ln x and g = f ^(-1) then correct statement (s) is/are:

If f is a real function defined by f(x)=(log(2x+1))/(sqrt3-x) , then the domain of the function is

Let f:R->[1,oo) be defined as f(x)=log_10(sqrt(3x^2-4x+k+1)+10) If f(x) is surjective then k =

Let f:R->[1,oo) be defined as f(x)=log_10(sqrt(3x^2-4x+k+1)+10) If f(x) is surjective then k =

If f(x)=|log_(e) x|,then

Prove that the function f: R^(+) to R which is defined as f(x)=log_(e) x is one - one .

RESONANCE ENGLISH-RELATION, FUNCTION & ITF-SCQ_TYPE
  1. Which of the following pair of functions are identical ?

    Text Solution

    |

  2. If domain of f(x) is(-oo,0), then domain of f(6{x}^2-5(x)+ 1) is (wher...

    Text Solution

    |

  3. Let f: (e, oo) -> R be defined by f(x) =ln(ln(In x)), then

    Text Solution

    |

  4. If f(x) =2 [x]+ cos x, then f: R ->R is: (where [ ] denotes greatest ...

    Text Solution

    |

  5. If f:R to R, f(x) ={(x|x|-4", "x in Q),(x|x|-sqrt(3)", "x notin Q...

    Text Solution

    |

  6. f(x) = |x-1|, f: R^+->R, g(x) = e^x, g:[-1,oo)->R. If the function fog...

    Text Solution

    |

  7. Let f:(2,4)->(1,3) where f(x) = x-[x/2] (where [.] denotes the greates...

    Text Solution

    |

  8. Find the condition so that the function f(x)=x^(3)+ax^(2)+bx+c is an i...

    Text Solution

    |

  9. If the function f:[1,\ oo)->[1,\ oo) defined by f(x)=2^(x(x-1)) is inv...

    Text Solution

    |

  10. f:N to N, where f(x)=x-(-1)^(x), Then f is

    Text Solution

    |

  11. tan ((pi)/(4) + (1)/(2) cos^(-1) x) + tan ((pi)/(4) - (1)/(2) cos^(-1)...

    Text Solution

    |

  12. The value of cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1...

    Text Solution

    |

  13. The domain of the function f (x) = sin^(-1)((1+x^3)/(2x^(3/2)))+sqrt(s...

    Text Solution

    |

  14. A function g(x) satisfies the following conditions (i) Domain of g i...

    Text Solution

    |

  15. The complete solution set of the inequality [cot^(-1)x]^2-6[cot^(-1)x]...

    Text Solution

    |

  16. sin^-1(sin 5)> x^2-4 x holds if

    Text Solution

    |

  17. If sin^(-1)(x-(x^2)/2+(x^3)/4-ddot)+cos^(-1)(x^2-(x^4)/2+(x^6)/4)=pi/2...

    Text Solution

    |

  18. If cot^(-1) (sqrt(cos alpha)) - tan^(-1) (sqrt(cos alpha)) = x, then s...

    Text Solution

    |

  19. The trigonometric equation sin^(-1) x = 2 sin^(-1) a has a solution fo...

    Text Solution

    |

  20. If f(x)=cot^-1 x ; R^+ -> (0,pi/2) and g(x)=2x-x^2 ; R-> R . Then t...

    Text Solution

    |