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)

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- Jun 21st 2009, 09:17 AMfadeerhow 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) - Jun 21st 2009, 09:29 AMTwig
hi

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

This is true for $\displaystyle |x| \leq 1 $

So $\displaystyle D_{g \, \circ f} = x: |x| \leq 1 $ - Jun 21st 2009, 09:40 AMfadeerThanks
Thank u

But what abt the range of the inner function?

How does it interfere in the solution?

Sorry abt bothering u. - Jun 22nd 2009, 01:01 AMTwig
You need the range of the inner function to be the domain of the outer function. And since the function $\displaystyle g $ has domain $\displaystyle x \geq 0 $ , you need $\displaystyle (1-x^{2}) \geq 0$ .

This requires $\displaystyle |x|\leq 1 $

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