Home
Class 12
MATHS
If f: A->B is an injection such that ...

If `f: A->B` is an injection such that range of `f={a}` . Determine the number of elements in `A` .

Text Solution

Verified by Experts

Range of `f={a}`
So the number of images of `f=1`
Since, `f` is an injective, there will be exactly one image for each element of `f`.
So, the number of elements in `A=1`
Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

Similar Questions

Explore conceptually related problems

If f:A rarr B is an injection such that range of f={a}. Determine the number of elements in A.

Let m be the number of elements in the domain of f(x) and n be the number of elements in the range of f(x) where f(x)=sin^(-1)[sec(3tan^(-1)x)]+cos^(-1)[cos ec(3cot^(-1)x)] ,then the value of (m+n) is:

Let f be real valued function from N to N satisfying. The relation f(m+n)=f(m)+f(n) for all m,n in N . If domain of f is first 3m natural numbers and if the number of elements common in domain and range is m, then the value of f(1) is

The atomic number of 5f series range from

If f:x rarr y, where x and y are sets containing natural numbers,f(x)=(x+5)/(x+2) then the number of elements in the domain and range of f(x) are,respectively.(a) 1 and 1( b) 2 and 1(c)2 and 2(d)1 and 2

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Classify f: R->R , defined by f(x)=1+x^2 as injection, surjection o...

    Text Solution

    |

  2. Classify f: R->R , defined by f(x)=x/(x^2+1) as injection, surjecti...

    Text Solution

    |

  3. If f: A->B is an injection such that range of f={a} . Determine the...

    Text Solution

    |

  4. Show that the function f: R-{3}->R-{1} given by f(x)=(x-2)/(x-3) is a ...

    Text Solution

    |

  5. Let A=[-1,\ 1] . Then, discuss whether the following functions from...

    Text Solution

    |

  6. Are the following set of ordered pairs functions? If so, examine wh...

    Text Solution

    |

  7. Let A={1,\ 2,\ 3} . Write all one-one from A to itself.

    Text Solution

    |

  8. If f: R->R be the function defined by f(x)=4x^3+7 , show that f is a b...

    Text Solution

    |

  9. Show that the exponential function f: R->R , given by f(x)=e^x , is ...

    Text Solution

    |

  10. Show that the logarithmic function f: R0+->R given by f(x)=(log)a x...

    Text Solution

    |

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

    Text Solution

    |

  12. If A={1,\ 2,\ 3} , show that an onto function f: A->A must be one-o...

    Text Solution

    |

  13. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

    Text Solution

    |

  14. Give examples of two one-one functions f1 and f2 from R to R such t...

    Text Solution

    |

  15. Give examples of two surjective function f1 and f2 from Z to Z such...

    Text Solution

    |

  16. Show that if f1 and f2 are one-one maps from R to R , then the product...

    Text Solution

    |

  17. Suppose f1 and f2 are non-zero one-one functions from R to R . Is (...

    Text Solution

    |

  18. Given A={2,\ 3,\ 4} , B={2,\ 5,\ 6,\ 7} . Construct an example of a...

    Text Solution

    |

  19. Given A={2,\ 3,\ 4} , B={2,\ 5,\ 6,\ 7} . Construct an example of a...

    Text Solution

    |

  20. Given A={2,\ 3,\ 4} , B={2,\ 5,\ 6,\ 7} . Construct an example of a...

    Text Solution

    |