Home
Class 11
MATHS
Let f,\ g be two real functions defined ...

Let `f,\ g` be two real functions defined by `f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot` Then describe each of the following function: `2f-sqrt(5)g`

Text Solution

Verified by Experts

`(2f-sqrt(5)g)(x)=2f(x)-sqrt(5)g(x)`
`=2sqrt(x+1)-sqrt(5)(9-x^2)`
`=2sqrt(x+1)-sqrt(45-5x^2)`
The domain of `2f-sqrt(5)g`=domain of `f` `cap` domain of `g`
`[-1, oo) cap [-3, 3]`
`=[-1, 3]`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    RD SHARMA|Exercise Solved Examples And Exercises|97 Videos

  • GEOMETRIC PROGRESSIONS

    RD SHARMA|Exercise Solved Examples And Exercises|255 Videos

Similar Questions

Explore conceptually related problems

Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot Then describe each of the following function: f+g

Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot Then describe each of the following function: g-f

Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot Then describe each of the following function: f\ g

Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot Then describe each of the following function: f//g

Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot Then describe each of the following function: g/f

Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot Then describe each of the following function: f^2+7f

Let f\ a n d\ g\ be real functions define by f(x)=x+2 and g(x)=4-x^2dot Then, find each of the following function: f+g

Let f\ a n d\ g\ be real functions define by f(x)=x+2 and g(x)=4-x^2dot Then, find each of the following function: f-g

Let f\ a n d\ g\ be real functions define by f(x)=x+2 and g(x)=4-x^2dot Then, find each of the following function: f/g

Let f\ a n d\ g\ be real functions define by f(x)=x+2 and g(x)=4-x^2dot Then, find each of the following function: fg

RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)...

    Text Solution

    |

  2. Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)...

    Text Solution

    |

  3. Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)...

    Text Solution

    |

  4. Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)...

    Text Solution

    |

  5. If f,\ g,\ h are real functions defined by f=sqrt(x+1),\ g(x)=1/x\ a n...

    Text Solution

    |

  6. Let f, g : R -> R be defined, respectively by f(x)=x+1 ,g(x)=2x-3 . Fi...

    Text Solution

    |

  7. Le f:[0,\ oo)->R\ a n d\ g: R->R be defined by f(x)=sqrt(x) and g(x)=x...

    Text Solution

    |

  8. Let f(x)=x^2 and g(x)" "=" "2x" "+" "1 be two real functions....

    Text Solution

    |

  9. Write the range of the real function f(x)=|x|dot

    Text Solution

    |

  10. If f(x)=1-1/x then write the value of f(f(1/x))dot

    Text Solution

    |

  11. If f(x)=4x-x^2, x in R , then write the value of f(a+1)-f(a-1)dot

    Text Solution

    |

  12. If f,\ g,\ h are real functions given by f(x)=x^2,g\ (x)=tanx\ a n d\ ...

    Text Solution

    |

  13. Write the domain and range of function f(x) given by f(x)=1/(sqrt(x-[x...

    Text Solution

    |

  14. Write of the domain and range of f(x)=sqrt(x-[x])dot

    Text Solution

    |

  15. Write the domain and range of function f(x) given by f(x)=sqrt([x]-x).

    Text Solution

    |

  16. Let A and B be any two sets such that n(B)=P, n(A)=q then the total nu...

    Text Solution

    |

  17. Find the values of x for which the functions f(x)=3x^2-1 and g(x)=3+x ...

    Text Solution

    |

  18. If f(x)="cos"((log)e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value ...

    Text Solution

    |

  19. Let f(x)=|x-1|dot Then (a)f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c)f(...

    Text Solution

    |

  20. If A={1,2,3},\ B={x , y} , then the number of functions that can be de...

    Text Solution

    |