Home
Class 12
MATHS
Let f: R->R and g: R->R be defined by f(...

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

Text Solution

Verified by Experts

Given,` f(x)=x^2` and `g(x)=(x+1) `
`(gof)(x)=g{f(x)}=g(x^2)=(x^2+1).`
`(fog)(x)=f{g(x)}=f(x+1)=(x+1)^2`
Hence, `gofne=fog`
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:R rarr R and g:R rarr R be defined by f(x)=x^(2) and g(x)=x+1. Show that fog != gof

Let f:R rarr R and g:R rarr R be defined by f(x)=x+1 and g(x)=x-1. Show that fog =gof=I_(R)

Let f:R rarr and g:R rarr R be defined by f(x)=x+1 and g(x)=x-1. Show that fog =gof=I_(R) .

If f: R->R and g: R->R be functions defined by f(x)=x^2+1 and g(x)=sinx , then find fog and gof .

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

Let f: R->R , g: R->R be two functions defined by f(x)=x^2+x+1 and g(x)=1-x^2 . Write fog\ (-2) .

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 .

Let R^+ be the set of all non-negative real numbers. If f: R^+\ ->R^+ and g: R^+\ ->R^+ are defined as f(x)=x^2 and g(x)=+sqrt(x) . Find fog and gof . Are they equal functions.

Let R be the set of real number and the mapping f :R to R and g : R to R be defined by f (x)=5-x^(2)and g (x)=3x-4, then the value of (fog) (-1) is

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Find fog\ (2) and gof\ (1) when: f: R->R ; f(x)=x^2+8 and g: R->R ; g(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Let f(x)=[x] and g(x)=|x| . Find (f+2g)(-1)

    Text Solution

    |

  18. Let fa n dg be real functions defined by f(x)=x/(x+1)a n dg(x)=1/(x+3)...

    Text Solution

    |

  19. If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

    Text Solution

    |

  20. If f(x)=1/(2x+1),\ x!=-1/2,\ then show that f(f(x))=(2x+1)/(2x+3) , p...

    Text Solution

    |