# Math Help - how to find domain

1. ## 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.

2. 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 $D_{g \, \circ f} = x: |x| \leq 1$

3. ## Thanks

Thank u

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

Sorry abt bothering u.

4. 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, $D_{g\, \circ f} = [-1,1]$