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

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos
  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

Similar Questions

Explore conceptually related problems

If f: AvecB is an injection such that range of f={a}dot Determine the number of elements in Adot

If A = {9, 10, 11, 12, 13} and let f : A rarr N is defined by f(x) = highest prime factor of x. then the number of distinct elements in the image of f is : "(a) 6 (b)7 (c) 8 (d) 4 "

If A and B be two sets such that n(A) = 15, n(B)=25 then number of elements of elements in the range of n(A Delta B) (symmetric difference of A and B ) is

If f:x->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

If f(x) is a polynomial such that f(a)f(b)<0, then what is the number of zeros lying between a and b ?

f(x)=sinx+cosx+3 . find the range of f(x).

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

Let A and B be two sets having 4 and 7 elements respectively. Then write the maximum number f elements that AuuB can have:

Let f: R->R and g: R->R be two given functions such that f is injective and g is surjective. Then which of the following is injective? (a) gof (b) fog (c) gog (d) none of these

Where a, b,c, d, e,f,g, h ar 3^(rd) period elements. If difference between atomic number of elements b and e is x and difference between atomic number of elements c and f is y . What is the value of x-y .

RD SHARMA ENGLISH-FUNCTION-All Questions
  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

    |