Home
Class 12
MATHS
If the functions f, g and h are defined ...

If the functions f, g and h are defined from the set of real numbers R to R such that
`f(x)=x^(2)-1,g(x)=sqrt((x^(2)+1))`,
`h(x)={{:("0,","if",xle0),("x,","if",xge0):}`
Then find the composite function hofog and determine whether the function fog is invertible and h is the identity function.

Promotional Banner

Topper's Solved these Questions

  • Function

    A DAS GUPTA|Exercise Exercise|57 Videos

  • Equations, Inequation and Expressions

    A DAS GUPTA|Exercise Exercise|301 Videos

  • Heights and Distances

    A DAS GUPTA|Exercise Exercise|3 Videos

Similar Questions

Explore conceptually related problems

Let the function f, g, h are defined from the set of real numbers RR to RR such that f(x) = x^2-1, g(x) = sqrt(x^2+1), h(x) = {(0, if x lt 0), (x, if x gt= 0):}. Then h o (f o g)(x) is defined by

"If "f:R to R, g:R and h:R to R be three functions are given by f(x)=x^(2)-1,g(x)=sqrt(x^(2)+1)and h(x)={{:(,0,x le0),(,x,xgt 0):} Then the composite functions (ho fog) (x)) is given by

If the functions f and g defined from the set of real number R to R such that f(x) = e^(x) and g(x) = 3x - 2, then find functions fog and gof. Also, find the domain of the functions (fog)^(-1) and (gof)^(-1) .

R be set of real numbers the function f:R^()rarr R f(x)=log|x+sqrt(1+x^(2))| then range of f(x) is

If f,g,\ h are three functions defined from R\ to\ R as follows: the range of h(x)=x^2+1

If f,g,\ h are three functions defined from R\ to\ R as follows: Find the range of f(x)=x^2

A DAS GUPTA-Function-Exercise
  1. If the functions f, g and h are defined from the set of real numbers R...

    Text Solution

    |

  2. Let f(x)=(ax+b)/(cx+d) , x!=-d/c. If d=-a, show that f{(x)}=x is an ...

    Text Solution

    |

  3. If f(x)=loge(x+sqrt(1+x^2) , g(x)=loge(1+sqrt(1+x^2)and h(x)=f(x)-g(x...

    Text Solution

    |

  4. Find the natural number a for which sum(k=1)^n f(a+k)=16(2^n-1) wher...

    Text Solution

    |

  5. Find the domain of f(x)=sqrt(x^2-4x+3)

    Text Solution

    |

  6. Find the domain off(x)=1/sqrt(x^2-x-2)

    Text Solution

    |

  7. Find the domain of f(x)=1/(sqrt(x-|x|))

    Text Solution

    |

  8. Find the domain off(x)=sqrt(((x+1)(x-3))/(x-2)

    Text Solution

    |

  9. Find the domain of f(x) = sqrt(log(10)((3-x)/x))

    Text Solution

    |

  10. Find the domain off(x)=sin^-1{log2(1/2x^2)}

    Text Solution

    |

  11. Find the domain ofy=cos^-1((3+sinx)/4)

    Text Solution

    |

  12. Find the domain off(x)=sqrt(5(|x|-x^2-6)

    Text Solution

    |

  13. Find the domain ofy=cos^-1{x[x[}

    Text Solution

    |

  14. Find the domain off(x)=log2x-5(x-3x-10)

    Text Solution

    |

  15. Find the domain of the real-valued functions: f(x)=sqrt(4-x)+sqrt(x-5)

    Text Solution

    |

  16. Find the domain of the real-valued functions: f(x)=sqrt(3-x)+cos^-(1)(...

    Text Solution

    |

  17. Find the domain of the real-valued functions: y=sin^-1x+sqrt(2x-x^2)-1...

    Text Solution

    |

  18. If log(x)y.log(xy)y.log(x^2y)y=1/6 then express y as the real function...

    Text Solution

    |

  19. f(x) is defined over [0,1]. Find the domain of the function f(2x+3)

    Text Solution

    |

  20. The function f(x) is defined on the interval [0, 1]. Find the domain ...

    Text Solution

    |

  21. f(x) is defined over [0,1]. Find the domain of the function f(cosx)

    Text Solution

    |