Home
Class 12
MATHS
If f: AvecBa n dg: BvecC are one-one ...

If `f: AvecBa n dg: BvecC` are one-one functions, show that `gof` is one-one function.

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: A->B and g: B->C are one-one functions, show that gof is one-one function.

What is meant by one-one function?

Statement-1 : If f(x) and g(x) are one-one functions then f(g(x)) and g(f(x)) is also a one-one function. and Statement-2 The composite function of two one-one function may or many not be one-one.

If fa n dg are one-one functions, then (a) f+g is one one (b) fg is one one (c) fog is one one (d) non e of t h e s e

If f and g are one-one functions, then a. f+g is one one b. fg is one one c. fog is one one d. none of these

Let A be a finite set. If f: AvecA is an onto function, show that f is one-one also.

Which of the functions defined below is one one function ?

if f(g(x)) is one-one function, then

Let A be a finite set. If f: A->A is a one-one function, show that f is onto also.

Let A be a finite set. If f: A->A is an onto function, show that f is one-one also.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If f: A->B and g: B->C are onto functions show that gof is ...

    Text Solution

    |

  2. Show that the logarithmic function f: R0+vecR given by f(x)=(log)a ...

    Text Solution

    |

  3. If f: AvecBa n dg: BvecC are one-one functions, show that gof is on...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor on...

    Text Solution

    |

  7. Suppose f1a n df2 are non-zero one-one functions from RtoRdot is (f1...

    Text Solution

    |

  8. Let f={(3,\ 1),\ (9,\ 3),\ (12 ,\ 4)} and g ={(1,\ 3),\ (3,\ 3),\ (4,\...

    Text Solution

    |

  9. Find fog(2) and gof(1) when: f: R rarr R ;f(x)=x^2+8 and g: R rarr ...

    Text Solution

    |

  10. Let f: RvecR and g: RvecR be defined by f(x)=x^2 and g(x)=x+1. Show ...

    Text Solution

    |

  11. Let R^+ be the set of all non-negative real numbers. if f: R^+ rar...

    Text Solution

    |

  12. Let L be the line of intersection of the planes 2x""+""3y""+""z""=""...

    Text Solution

    |

  13. Let f: RrarrR and g: RrarrR be defined by f(x)=x+1 and g(x)=x-1....

    Text Solution

    |

  14. Show that the exponential function f: R to R , given by f(x)=e^x , i...

    Text Solution

    |

  15. Let A="{"-1,0,1")"a n df={(x , x^2): xA}dot Show that f: AvecA is neit...

    Text Solution

    |

  16. If f: AvecB is an injection such that range of f={a}dot Determine t...

    Text Solution

    |

  17. Which of the following functions from AtoB are one-one and onto? ...

    Text Solution

    |

  18. Prove that the function F : NtoN , defined by f(x)=x^2+x+1 is one-on...

    Text Solution

    |

  19. Let A be any non-empty set. Then, prove that the identity function on ...

    Text Solution

    |

  20. Let A=R-[2] \ a n d \ B=R-[1]. If f: A->B is a mapping defined by f(x)...

    Text Solution

    |