Home
Class 12
MATHS
If f:R to R is an invertible function su...

If `f:R to R` is an invertible function such that `f(x)` and `f^(-1)(x)` are symmetric about the line `y= -x,` then

A

`f(x)` is odd

B

`f(x)` and `f^(-1)(x)` may not be mirror image about the line `y=x`

C

`f(x)` may not be odd

D

`f(x)` is even

Text Solution

Verified by Experts

The correct Answer is:
A
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

If f: R->R is an invertible function such that f(x) and f^-1(x) are symmetric about the line y=-x, then (a) f(x) is odd (b) f(x) and f^-1(x) may be symmetric (c) f(c) may not be odd (d) none of these

If f: Rvec is an invertible function such that f(x)a n df^(-1)(x) are symmetric about the line y=-x , then f(x)i sod d f(x)a n df^(-1)(x) may not be symmetric about the line y=x f(x) may not be odd non eoft h e s e

If the graph of a function f(x) is symmetrical about the line x = a, then

If the graph of the function y = f(x) is symmetrical about the line x = 2, then

If f: R->R is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

If f: R to R is defined as f(x)=2x+5 and it is invertible , then f^(-1) (x) is

f : R -> R is one-one, onto and differentiable and graph of y = f (x) is symmetrical about the point (4, 0), then

Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

If f(x) is an even function, then the curve y=f(x) is symmetric about

f:R to R is a function defined by f(x)= 10x -7, if g=f^(-1) then g(x)=

RESONANCE ENGLISH-RELATION, FUNCTION & ITF-SCQ_TYPE
  1. The inverse of the function f(x)=(e^(x)-e^(-x))/(e^(x)+e^(-x))

    Text Solution

    |

  2. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

    Text Solution

    |

  3. If f:R to R is an invertible function such that f(x) and f^(-1)(x) are...

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Find the domain of the function: f(x)=sin^(-1)(|x-1|-2)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. "cosec"^(-1)(cosx) is real , if :

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. If sin^(-1) x + sin^(-1) y = (2pi)/3", then " cos^(-1) x + cos^(-1) y

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |