Home
Class 12
MATHS
If the function f: RvecR be given by f(x...

If the function `f: RvecR` be given by `f(x)=x^2+2a n dg: RvecR` be given by `g(x)=x/(x-1)` . Find `foga n dgofdot`

Text Solution

Verified by Experts

`f: R -> R`
` f(x)=x^{2}+2`
` g: R -> R`
` g(x)=frac{x}{x-1}`
` fog (x)=f(g(x)) `
` =f(frac{x}{x-1})`
` =(frac{x}{x-1})^{2}+2`
` =frac{x^{2}}{x^{2}-2 x+1}+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

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:RrarrR be given by f(x)=x^(2)+2 and g:RrarrR be given by g(x)=(x)/(x-1),xne1 , find fog and gof and hence find fog (2) and gof (-3).

If the function f:R rarr A given by f(x)=(x^(2))/(x^(2)+1) is surjection,then find A

If a function f (x) is given as f (x) =x ^(2) -3x +2 for all x in R, then f (-1)=

Check the injectivity and surjectivity of the following functions: (i) f" ":" "N ->N given by f(x)=x^2 (ii) f" ":" "Z-> Z given by f(x)=x^2 (iii) f" ":" "R ->R given by f(x)=x^2 (iv) f" ":" "N-> N given by f(x)=x^3 (v) f" ":" "Z ->

The function f(x) given by f(x)=sin^(-1)((2x)/(1+x^(2))) is

Show that the function f:N rarr N, given by f(x)=2x, is one-one but not onto.

The domain of the function f given by f(x) = (x^(2)+ 2x+ 1)/(x^(2) - 5x+6)

Find the domain and range of the function f given by f(x) = x^2/(1-x^2)

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Given examples of two one-one functions f1a n df2 from R to R such ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Let f and g be real functions defined by f(x)=x/(x+1) a n d g(x)=x/(1...

    Text Solution

    |