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.
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] $