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Math Help - how to find domain

  1. #1
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    how to find domain

    Hi, could anyone be kind enough to tell me how to find domain of gof (x):

    f(X)= 1-x^2, x is any no. in R
    g(x)= 2x, x >= 0

    Thanks a lot.
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  2. #2
    Senior Member Twig's Avatar
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    hi

    Since you need  x \geq 0 for  g(x) , then we must have  (1-x^{2}) \geq 0

    This is true for  |x| \leq 1

    So D_{g \, \circ f} = x: |x| \leq 1
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  3. #3
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    Thanks

    Thank u

    But what abt the range of the inner function?
    How does it interfere in the solution?

    Sorry abt bothering u.
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  4. #4
    Senior Member Twig's Avatar
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    You need the range of the inner function to be the domain of the outer function. And since the function  g has domain  x \geq 0 , you need  (1-x^{2}) \geq 0 .

    This requires  |x|\leq 1

    So,  D_{g\, \circ f} = [-1,1]
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