Home
Class 12
MATHS
Find gof and fog , if f: R->R and g: R->...

Find `gof` and `fog` , if `f: R->R` and `g: R->R` are given by `f(x)=|x|` and `g(x)=|5x-2|` .

Text Solution

Verified by Experts

Given:
`f(x)=|x|` and `g(x)=|5x-2|`
`f(g(x))=|g(x)|`
`fog(x)=||5x-2||`
`fog(x)=|5x-2|`
`g(f(x))=|5f(x)-2|`
`gof(x)=|5|x|-2|`
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

Find gof and fog, if f" ":" "R ->R and g" ":" "R ->R are given by f(x)" "=" "cos" "x and g(x)=3x^2 . Show that gof!=fog .

Find gof and fog when f: R->R and g: R->R is defined by f(x)=x^2+2x-3 and g(x)=3x-4

Find gof and fog when f: R->R and g: R->R is defined by f(x)=x and g(x)=|x|

Find gof and gof when f: R->R and g: R->R is defined by f(x)=8x^3 and g(x)=x^(1//3)

Find gof and gof when f: R->R and g: R->R is defined by f(x)=2x+3 and g(x)=x^2+5

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

Find gof and fog wehn f:R rarr R and g:R rarr R are defined by f(x)=2x+3 and g(x)=x^(2)+5f(x)=2x+x^(2) and g(x)=x^(3)f(x)=x^(2)+8 and g(x)=3x^(3)+1f(x)=8x^(3) and g(x)=x^(1/3)+1f(x)=8x^(3) and

If f:R rarr R and g:R rarr R given by f(x)=x-5 and g(x)=x^(2)-1, Find fog

Let f: R->R and g: R->R be defined by f(x)=x^2 and g(x)=x+1 . Show that fog!=gofdot

Find fog and g o f when f : R → R and g : R → R is defined by f ( x ) = 5 x + x^2 and g ( x ) = 2x

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Let f:{2,3,4,5}vec{3,4,5,9}a n dg:{3,4,5,9}vec{7, 11 , 15} be function...

    Text Solution

    |

  2. Let f:{1,\ 3,4\ }->{1,\ 2,\ 5} and g:{1,\ 2,\ 5}->{1,\ 3} be given by ...

    Text Solution

    |

  3. Find gof and fog , if f: R->R and g: R->R are given by f(x)=|x| and g(...

    Text Solution

    |

  4. If the functions f and g are given by f={(1,\ 2),\ (3,\ 5),\ (4,\ 1)} ...

    Text Solution

    |

  5. If the function f: R->R be given by f(x)=x^2+2 and g: R->R be given by...

    Text Solution

    |

  6. If f: R-{7/5}->R-{3/5} be defined as f(x)=(3x+4)/(5x-7) and g: R-{3/5}...

    Text Solution

    |

  7. If f: R ->Ris defined by f(x) = x^2- 3x + 2, find f(f(x)).

    Text Solution

    |

  8. If f,g: RvecR are defined respectively by f(x)=x^2+3x+1,g(x)=2x-3, fin...

    Text Solution

    |

  9. Let f: Z->Z be defined by f(x)=x+2. Find g: Z->Z such that gof=IZ .

    Text Solution

    |

  10. If f: Z->Z be defined by f(x)=2x for all x in Z . Find g: Z->Z such t...

    Text Solution

    |

  11. Let f,\ g and h be functions from R to R . Show that (f+g)oh=foh+goh

    Text Solution

    |

  12. Let f,\ g and h be functions from R to R . Show that (fg)oh=(foh)(goh)

    Text Solution

    |

  13. Let f: R->R be the signum function defined as f(x)={1,\ x >0,\ \ \ \ 0...

    Text Solution

    |

  14. Let A={x in R :0lt=xlt=1}dot If f: AvecA is defined by f(x)={x ,ifx Q...

    Text Solution

    |

  15. Let f: RvecR and g: vecR be two functions such that fog(x)=sinx^2a n...

    Text Solution

    |

  16. If f: R->R be given by f(x)=sin^2x+sin^2(x+pi//3)+cosx\ cos(x+pi//3) f...

    Text Solution

    |

  17. Let f: ZvecZ be defined by f(n)=3n for all n in Z and g: Zvec be defi...

    Text Solution

    |

  18. Let f: RvecR be a function given by f(x)=a x+b for all x in R . Find ...

    Text Solution

    |

  19. Let f: A->A be a function such that fof=f . Show that f is onto if and...

    Text Solution

    |

  20. Let f,g: RvecR be two functions defined as f(x)=|x|+x and g(x)=|x|-x ,...

    Text Solution

    |