Home
Class 12
MATHS
Find fog(2) and gof(1) when: f: R rarr...

Find `fog(2)` and `gof(1)` when: `f: R rarr R ;f(x)=x^2+8` and `g: R rarr R ;g(x)=3x^3+1.`

Text Solution

Verified by Experts

Given ` f(x) = x^2 + 8` and `g(x) = 3x^3 + 1. `
So,
`(fog)(2) = f(g(2)) `
`= f(3 × 2^3 + 1) `
`= f(3 × 8 + 1) `
...
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 f o g ( 1 ) when: f : R → R ; f ( x ) = x^2 +8 and g:R→R ;g(x)=3 x^3 +1 .

Find fog\ (2) and gof\ (1) when: f: R->R ; f(x)=x^2+8 and g: R->R ; g(x)=3x^3+1 .

Let :R rarr R;f(x)=sin x and g:R rarr Rg(x)=x^(2) find fog and gof.

If f:R rarr R,f(x)=2x-1 and g:R rarr R,g(x)=x^(2) then (gof)(x) equals

If f:R rarr R,f(x)=2x;g:R rarr Rg(x)=x+1, then (f*g)(2) equals

Let R be the set of real numbes.If f:R rarr R;f(x)=x^(2) and g:R rarr R;g(x)=2x+1. Then,find fog and gof .Also,show that fog!= gof.

If the function f:R rarr R be given by f(x)=x^(2)+2 and g:R rarr R be given by g(x)=(x)/(x-1). Find fog and gof

If the function f:R rarr R be given by f(x)=x^(2)+2 and g:R rarr R be given by g(x)=(x)/(x-1). Find fog and gof.

Let R be the set of real numbers.If f:R rarr R:f(x)=x^(2) and g:R rarr R;g(x)=2x+1. Then,find fog and gof . Also,show that fog!=gof .

If the function f: R rarr R be defined by f(x)=2x-3 and g:R rarr R by g(x)=x^(3)+5 , then show that fog is invertible. Also find (fog)^(-1)(x) , hence find (fog)^(-1)(9) .

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |