Home
Class 12
MATHS
Let f={(3,\ 1),\ (9,\ 3),\ (12 ,\ 4)} an...

Let `f={(3,\ 1),\ (9,\ 3),\ (12 ,\ 4)}` and `={(1,\ 3),\ (3,\ 3),\ (4,\ 9),\ ` `(5,\ 9)}` . Show that `gof` and `fog` are both defined. Also, find `fog` and `gofdot`

Text Solution

Verified by Experts

`f: {3, 9, 12} → {1, 3, 4}` and `g: {1, 3, 4, 5} → {3, 9} `
Co-domain of f is a subset of the domain of g.
So,
`(gof) (3) = g(f(3)) = g(1) = 3 `
...
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

Let f={(1,-1),(4,-2),(9,-3),(16 ,4)} and g={(-1,-2),(02 ,-4),(-3,-6),(4,8)}dot Show that gof is defined while fog is not defined. Also, find gofdot

f={(1,2),(3,-2),(-1,1)} and g={(2,3),(-2,1),(1,3)} Prove that (gof) and (fog) are both defined.Also find (gof) and (fog) as sets of ordered pairs

Let A ={2,3,4,5} " and " ={7,9,11,13} and let f = {(2,7),(3,9) ,(4,11),(5,13)} Show that f is invertible and find f^(-1)

If f = {(1,4), (2,5),(3,5) and g ={(4,8),(5,7),(6,9)}, then gof is

If f={(1,4),(2,5),(3,6)} and g={(4,8),(5,7),(6,9)} , then gof is

Let A = {1,2,3,4}, B = { 1,5,9,11,15,16} and f = {(1,5), (2,9),(3,1),(4,5),(2,11)}. Then ,

If A = ({:(9, -7), (-4, 3):}) " and B"=({:(-3, -7),(-4, -9):}) , then find AB and hence find A^(-1) .

If the mapping f and g are given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, write down pairs in the mapping fog and gof.

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Find gof and fog when f: R->R and g: R->R is defined by f(x)=x^2+2x-3 ...

    Text Solution

    |

  2. Find gof and gof when f: R->R and g: R->R is defined by f(x)=8x^3 and ...

    Text Solution

    |

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

    Text Solution

    |

  4. Let f={(1,-1),(4,-2),(9,-3),(16 ,4)} and g={(-1,-2),(02 ,-4),(-3,-6),(...

    Text Solution

    |

  5. Let A={a ,\ b ,\ c} , B={u\ v ,\ w} and let f and g be two functions f...

    Text Solution

    |

  6. Find fog\ (2) and gof\ (1) when: f: R->R ; f(x)=x^2+8 and g: R->R ; g(...

    Text Solution

    |

  7. Let R^+ be the set of all non-negative real numbers. If f: R^+\ ->R...

    Text Solution

    |

  8. Let f: R->R and g: R->R be defined by f(x)=x^2 and g(x)=x+1 . Show tha...

    Text Solution

    |

  9. Let f: RvecR and g: RvecR be defined by f(x)=x+1 and g(x)=x-1. Show...

    Text Solution

    |

  10. Verify assoiativity for the following three mappings : f: NvecZ0...

    Text Solution

    |

  11. Consider f : N ->N, g : N ->Nand h : N ->Rdefined asf (x) = 2x, g (y) ...

    Text Solution

    |

  12. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

    Text Solution

    |

  13. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

    Text Solution

    |

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

    Text Solution

    |

  15. If f: R->R and g: R->R be functions defined by f(x)=x^2+1 and g(x)=sin...

    Text Solution

    |

  16. If f:[0,oo)vecRa n dg: RvecR be defined as f(x)=sqrt(x) and g(x)=-x^2-...

    Text Solution

    |

  17. If f(x)=e^x and g(x)=(log)e x(x >0), find foga n dgofdot Is fog=gof?

    Text Solution

    |

  18. If f(x)=sqrtx(x > 0) and g(x)=x^2-1 are two real functions, find fog a...

    Text Solution

    |

  19. If f(x)=1/x and g(x)=0 are two real functions, show that fog is not...

    Text Solution

    |

  20. Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3) fog(5/3)

    Text Solution

    |