Home
Class 12
MATHS
If f,g: RvecR are defined respectively b...

If `f,g: RvecR` are defined respectively by `f(x)=x^2+3x+1,g(x)=2x-3,` find fog (ii) gof (iii) fof (iv) gog.

Text Solution

AI Generated Solution

To solve the problem, we need to find the following composite functions based on the definitions of \( f(x) \) and \( g(x) \): 1. \( f(g(x)) \) 2. \( g(f(x)) \) 3. \( f(f(x)) \) 4. \( g(g(x)) \) Given: ...
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

If f,g:R rarr R are defined respectively by f(x)=x^(2)+3x+1 and g(x)=2x-3 then find the value of fog

If f, g : R rarr R be defined respectively by f(x) = 3x + 2 and g(x) = 6x + 5. Find f-g.

If f, g : R rarr R be defined respectively by f(x) = 8x + 7 and g(x) = 3x - 1. Find f-g.

Let f, g : R rarr R be defined respectively by f(x) = 2x + 3 and g(x) = x - 10. Find f-g.

If f(x)=3x+1,g(x)=x^(2)+2 find fog(x) and gof(x)

If f:RrarrR,g:RrarrR are defined by f(x)=3x-1 and g(x)=x^(2)+1 , then find (i) fof(x^(2)+1) (ii) fog(2) (iii) gof(2a-3)

Let f, g : R -> R be defined, respectively by f(x)" "=" "x" "+" "1 ,g(x)" "=" "2x" "" "3 . Find f" "+" "g," "f" "" "g and f/g .

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 .

If f:R rarr R and g:R rarr R are defined as follows: f(x)=x+2 and g(x)=2x^(2)+5 find,(i) fog and (ii) gof

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Show that if f1a n df1 are one-one maps from RtoR , then the pro...

    Text Solution

    |

  2. Given examples of two one-one functions f1a n df2 from R to R such ...

    Text Solution

    |

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

    Text Solution

    |

  4. If the function f: RvecR be given by f(x)=x^2+2a n dg: RvecR be given ...

    Text Solution

    |

  5. If the function fa n dg are given by f={(1,2),(3,5),(4,1)}a n dg="("(2...

    Text Solution

    |

  6. Suppose f1a n df2 are non=zero one-one functions from RtoRdot is (f...

    Text Solution

    |

  7. Find whether the following functions are one-one or not: f: Rvecgi...

    Text Solution

    |

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

    Text Solution

    |

  9. Discuss the surjectivity of the following functions: f: R-> given by ...

    Text Solution

    |

  10. Show that the function f: ZvecZ defined by f(x)=x^2+x for all x in Z ...

    Text Solution

    |

  11. Let A be the set of all 50 students of class XII in a central school. ...

    Text Solution

    |

  12. Show that the function f: RvecR defined by f(x)=3x^3+5 for all x in R...

    Text Solution

    |

  13. Show that the function f: RvecR given by f(x)=cosxfora l lx in R , is...

    Text Solution

    |

  14. Show that the function f: Rvec given by f(x)=x a+b , where a , b in R...

    Text Solution

    |

  15. If f(x) = x/(sqrt(1+x^2) then fofof(x)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Let f:R→R and g:R→R defined by f(x)=x 2 and g(x)=(x+1). Show that g...

    Text Solution

    |