Home
Class 12
MATHS
Let f(x) = sqrt(x) and g(x) = 1 -x^(2). ...

Let f(x) = `sqrt(x)` and g(x) = `1 -x^(2)`.
Show that hgof only on `R_(0)={x in R: x gt= 0}` and not on R..

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    MBD PUBLICATION|Exercise QUESTION BANK|171 Videos

  • RELATIONS AND FUNCTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|106 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = sqrt(1+x) , g(x) = sqrt(1-x) Find f + g also find the domain of the each case.

Let f(x) = sqrt(1+x) , g(x) = sqrt(1-x) Find f - g also find the domain of the each case.

If f(x) = x +7 and g(x) = x-7, x in R then find fog (6).

Let f(x) = sqrt(1+x) , g(x) = sqrt(1-x) Find f^'/g also find the domain of the each case.

Show that f(x) = 3x + 5 is a strictly increasing function on R.

Let f(x) = e^(x)g(x) , g(0)=2 and g (0)=1 , then find f'(0) .

Show that the function f(x) = x^3- 3x^2 + 3x, x in R is increasing on R.

Show that f(x)=a^x "on" R.(a gt 0 "and" a != 1) functions are injective.

MBD PUBLICATION-RELATION AND FUNCTION-QUESTION BANK
  1. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

    Text Solution

    |

  2. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domain of h(x) = 1-...

    Text Solution

    |

  3. Let f(x) = sqrt(x) and g(x) = 1 -x^(2). Show that hgof only on R(0)=...

    Text Solution

    |

  4. Find the composition fog and gof and test whether fog = gof when f and...

    Text Solution

    |

  5. Find the composition fog and gof and test whether fog = gof when f and...

    Text Solution

    |

  6. Find the composition fog and gof and test whether fog = gof when f and...

    Text Solution

    |

  7. Find the composition fog and gof and test whether fog = gof when f and...

    Text Solution

    |

  8. Let f be a real function. Show that h(x) =f(x)=f(-x) is always an even...

    Text Solution

    |

  9. Express each of 1+x+x^2 function as the sum of an even function and an...

    Text Solution

    |

  10. Express each of x^2 function as the sum of an even function and an odd...

    Text Solution

    |

  11. Express each of e^x function as the sum of an even function and an odd...

    Text Solution

    |

  12. Express each of e^x+ sin x function as the sum of an even function and...

    Text Solution

    |

  13. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

    Text Solution

    |

  14. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

    Text Solution

    |

  15. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

    Text Solution

    |

  16. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

    Text Solution

    |

  17. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

    Text Solution

    |

  18. Construct an example to show that f(A nn B )!= f(A) nn f(B) where A nn...

    Text Solution

    |

  19. Prove that for any f:X rarr Y , f o idx = f =idY of.

    Text Solution

    |

  20. Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...

    Text Solution

    |