Home
Class 12
MATHS
If f : X to Y is an invertible function,...

If f : X to Y is an invertible function, then which of the following is true?

A

f is one-one onto

B

f is one-one but not onto

C

f is onto but not one-one

D

None of these

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTION

    MODERN PUBLICATION|Exercise EXAMPLE|212 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|543 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXAMPLE|13 Videos

Similar Questions

Explore conceptually related problems

If y+log(1+x)=0 which of the following is true?

If A = [[a,b,c],[x,y,z],[p,q,r]], B= [[q , -b,y],[-p,a,-x],[r,-c,z]] and if A is invertible, then which of the following is not true?

f(x) is continuous at x = 0 then which of the following are always true ?

Let f : X rarr Y be an invertible function. Show that f has unique inverse.

Let f : X rarr Y be an invertible function. Show that the inverse of f^–1 is f, i.e. (f^–1)^–1 = f

Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f''(x)-2f'(x)+f(x) ≥e^x, x ∈[0,1] If the function e^(-x)f(x) assumes its min in the interval [0,1] at x=1/4 , which of the following is true?

If f(0)=f(1)=f(2)=0 and function f(x) is twice differentiable in (0, 2) and continuous in [0, 2], then which of the following is/are definitely true ?

Let f be a linear function with properties f(1)lef(2),f(3)gef(4)and f(5)=5, then which of the following is true

Let f : X rarr Y and g : Y rarr Z be two invertible functions. Then gof is also invertible with (gof)^–1 = f^ –1ofg^–1

MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. If f : X to Y is an invertible function, then which of the following i...

    Text Solution

    |

  2. Which one of the following graph represents the function of x? Why?

    Text Solution

    |

  3. Show that a one-one function f : {1, 2, 3} rarr {1, 2, 3} must be onto...

    Text Solution

    |

  4. Let A be the set of all 50 students of class XII in a school. Let f: A...

    Text Solution

    |

  5. Prove that the function f : RrarrR given by f (x) = 2x is one-one and...

    Text Solution

    |

  6. Show that the function: f: N rarr N given by f(1) = f (2) = 1 and f (x...

    Text Solution

    |

  7. Show that function f: Rrarr R given by f(x) = x^2 is neither one-one n...

    Text Solution

    |

  8. Show that f : NrarrN , given by : f(x) = {(x+1,,if x is odd,,),(x-1,,i...

    Text Solution

    |

  9. If f : R rarr R is defined by f(x) = x + 2, find f(f(x))

    Text Solution

    |

  10. If f : R rarr R be given by: f(x) = (3-x^3)^1//3, then f(f(x)) is:

    Text Solution

    |

  11. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find fog

    Text Solution

    |

  12. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find gof.

    Text Solution

    |

  13. Find gof and fog, if f(x) = |x| and g(x) = |5x -2|

    Text Solution

    |

  14. Let f(x) = (4x+3)/(6x-4), x ne 2/3 .show that fof (x) = x.

    Text Solution

    |

  15. Find gof and fog if f: RrarrR and g: R rarr R are given by f(x) = co...

    Text Solution

    |

  16. If the function f : R rarr R given by f(x) = x^2 +2 and g RrarrR be g...

    Text Solution

    |

  17. Let f : { 1, 2, 3} rarr {a, b, c} be one-one and onto function given b...

    Text Solution

    |

  18. Let A = R- {3} and B = R- {1}. If f: ArarrB is a function defined by ...

    Text Solution

    |

  19. Let Y = {n^2 : n in N} sub N Consider f : N rarr Y as f (n) = n^2 Show...

    Text Solution

    |

  20. Let f: Nrar R be a function defined as : f(x) = 4x^2 + 12 x + 15. Sho...

    Text Solution

    |

  21. Let f : N rarr N be a function deifned by f(x) = 9x^2 + 6x - 5. Show ...

    Text Solution

    |