Home
Class 12
MATHS
Let f be a function defined on [0,2]. Th...

Let `f` be a function defined on [0,2]. The prove that the domain of function `g(x)i sf(9x^2-1)dot`

Text Solution

Verified by Experts

The correct Answer is:
`[-(1)/(sqrt(3)),-(1)/(3)] cup [(1)/(3),(1)/(sqrt(3))]`
g is meaningful if
`0 le 9x^(2) -1 le 2 hArr 1 le 9x^(2) le 3`
i.e., ` x in [-(1)/(sqrt(3)),-(1)/(3)] cup [(1)/(3),(1)/(sqrt(3))]`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

The function f(x) is defined in 0 le x le1, find the domain of definition of f(x^2)

The function f(x) is defined in [0,1] . Find the domain of f(t a nx)dot

The function f(x) is defined in 0 le x le1, find the domain of definition of f(2x-1)

Find the domain of the function: f(x)=sin^(-1)(|x-1|-2)

The domain of the function f(x)=1/(sqrt(4x-|x^2-10 x+9|)) is

The domain of the function f(x)=(log)_(3+x)(x^2-1) is

Find the domain of the function : f(x)=sin^(-1)((log)_2x)

In the function f(x) is defined for x in[0,1] then the function f(2x+3) is defined for

The domain of the function f(x)=sin^(-1)(x-3)/sqrt(9-x^2) is

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. f(x) = (alpha x)/(x + 1) (x ne -1), then for what value of alpha , f{f...

    Text Solution

    |

  2. If the domain of y=f(x)i s[-3,2], then find the domain of g(x)=f(|[x]|...

    Text Solution

    |

  3. Let f be a function defined on [0,2]. The prove that the domain of fun...

    Text Solution

    |

  4. A function f has domain [-1,2] and range [0,1] . Find the domain and r...

    Text Solution

    |

  5. Let f(x)=tanx a n d g(f(x))=f(x-pi/4), where f(x)a n dg(x) are real ...

    Text Solution

    |

  6. Let g(x)=1+x-[x] and f(x)={-1,x < 0, 0, x=0 1, x > 0. Then for a...

    Text Solution

    |

  7. f(x)={(log(e)x",",0lt x lt 1),(x^(2)-1 ",",x ge 1):} and g(x)={(x+1","...

    Text Solution

    |

  8. The inverse of the function f(x)=(e^x-e^(-x))/(e^x+e^(-x))+2 is given ...

    Text Solution

    |

  9. Find the inverse of the function: f: R rarr (-oo,1)gi v e nb y\ f(x)=1...

    Text Solution

    |

  10. f:(2,3)->(0,1) defined by f(x)=x-[x],where[dot] represents the great...

    Text Solution

    |

  11. Find the inverse of the function: f:Z to Z defined by f(x)=[x+1], w...

    Text Solution

    |

  12. Find the inverse of the function: f(x)={(x^3-1, ,x<2), (x^2+3,xgeq2)}

    Text Solution

    |

  13. Find the inverse of the function: f:[-1,1]rarr[-1,1] defined byf(x)=x|...

    Text Solution

    |

  14. Find the inverse of the function: f:[1, oo) rarr [1,oo),w h e r ef(x)=...

    Text Solution

    |

  15. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R , d e t e...

    Text Solution

    |

  16. Let g(x) be a function such that g(a+b)=g(a)dotg(b)AAa , b in Rdot If...

    Text Solution

    |

  17. If f(x+2a)=f(x-2a),then prove that f(x) is periodic

    Text Solution

    |

  18. If f(x+f(y))=f(x)+yAAx ,y in R a n df(0)=1, then find the value of f(...

    Text Solution

    |

  19. If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

    Text Solution

    |

  20. Represent the following function:f: f ( x^2 + x + 3 ) + 2 f ( x^2 − 3 ...

    Text Solution

    |