how to find domain

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June 21st 2009, 09:17 AM
fadeer

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.(Clapping)
June 21st 2009, 09:29 AM
Twig

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 $D_{g \, \circ f} = x: |x| \leq 1$
June 21st 2009, 09:40 AM
fadeer

Thanks

Thank u

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

Sorry abt bothering u.
June 22nd 2009, 01:01 AM
Twig

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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