Home
Class 12
MATHS
Statement -1 All points of intersection ...

Statement -1 All points of intersection of `y=f(x)` and `y=f^(-1)(x)` lies on `y=x` only.
Statement -2 If point `P(alpha,beta)` lies on `y=f(x)` then `Q(beta,alpha)` lies on `y=f^(-1)(x)`.
Statement -3 Inverse of invertible function is unique and its range is equal to the function domain.
Which of the following option is correct for above statements in order

A

TTF

B

FTT

C

TTT

D

TFT

Text Solution

Verified by Experts

The correct Answer is:
C

NA
Promotional Banner

Topper's Solved these Questions

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise INTEGER_TYPE|21 Videos
  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise MCQ_TYPE|31 Videos
  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise MATCH THE COLUMN|5 Videos
  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos
  • SEQUENCE & SERIES

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

Similar Questions

Explore conceptually related problems

P(alpha,beta) lies on the line y=6x-1 and Q(beta,alpha) lies on the line 2x-5y=5 then the equation of line PQ is

The point of injtersection of the line x/p+y/q=1 and x/q+y/p=1 lies on the line

The graph of the function y=f(x) is shown in the adjacent figure then correct statement is

(alpha,beta) lies on the line y=6x-1 and Q(beta,alpha) lies on the line 2x-5y=5 ,then the equation of the line bar(PQ) is

I If a point (alpha,beta) lies on the circle x^(2)+y^(2)=1 then the locus of the point (3 alpha.+2,beta), is

Statement-1 : f(x) is a one-one function hArr f^(-1) (x) is a one-one function. and Statement-2 f^(-1)(x) is the reflection of the function f(x) with respect to y = x.

Consider the following statements : Statement 1 : The function f:IRtoIR such that f(x)=x^(3)" for all "x""inIR is one-one. Statement 2 : f(a)impliesf(b)" for all "a,binIR if the function f is one-one. Which one of the following is correct in respect of the above statements ?

Statement-1 If y=f(x) is increasing in [alpha,beta] , then its range is [f(alpha),f(beta)] Statement-2 Every increasing function need not to be continuous.

RESONANCE-RELATION, FUNCTION & ITF-SCQ_TYPE
  1. Let f(x)=(ax + b )/(cx+d). Then the fof (x)=x, provided that : (a!=0,...

    Text Solution

    |

  2. Let f(x)={(x,-1lexle1),(x^(2),1ltxle2):} the range of h^(-1)(x), where...

    Text Solution

    |

  3. Statement -1 All points of intersection of y=f(x) and y=f^(-1)(x) lies...

    Text Solution

    |

  4. The domain of definition of f(x)=sin^(-1)(|x-1|-2) is

    Text Solution

    |

  5. The function f(x)=cot^(-1)sqrt((x+3)x)+cos^(-1)sqrt(x^(2)+3x+1) is def...

    Text Solution

    |

  6. Domain of f(x)=cos^(-1)x+cot^(-1)x+cosec^(-1)x is

    Text Solution

    |

  7. Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is (pi/4,(3pi)/4) (b) [pi...

    Text Solution

    |

  8. cosec^(-1)(cos x) is real if

    Text Solution

    |

  9. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

    Text Solution

    |

  10. The solution of the equation sin^-1((tan)pi/4)-sin^-1(sqrt(3/x))-pi/6=...

    Text Solution

    |

  11. Number of solutions of the equation cot^(-1)sqrt(4-x^(2))+cos^(-1)(x^(...

    Text Solution

    |

  12. If pilexle2pi, then cos^(-1)(cosx) is equal to

    Text Solution

    |

  13. If sin^(-1)x+sin^(-1)y=(2pi)/3, then cos^(-1)x+cos^(-1)y is equal to

    Text Solution

    |

  14. lf x >=0 and theta = sin^(-1)x + cos^(-1)x-tan^(-1) x, then

    Text Solution

    |

  15. Number of solutions of equation tan^(-1)(e^(-x))+cot^(-1)(|lnx|)=pi//2...

    Text Solution

    |

  16. The numerical value of cot(2sin^(-1)\ 3/5+cos^(-1)\ 3/5) is

    Text Solution

    |

  17. Statement 1: tan^(2)(sec^(-1)2)+cot^(2)(cosec^(-1)3)=11. Statement -...

    Text Solution

    |

  18. If alpha is a real root of the equation x^(2)+3x-tan2=0 then cot^(-1)a...

    Text Solution

    |

  19. If sin^(-1)((sqrt(x))/2)+sin^(-1)(sqrt(1-x/4))+tan^(-1)y=(2pi)/3, then

    Text Solution

    |

  20. If xlt0, then value of tan^(-1)(x)+tan^(-1)(1/x) is equal to

    Text Solution

    |