Suppose that the domain of "$f$" function is equal to $[0,1]$, then find the domain of:
$f(3x^2)$ $f(1-x)$ and $f(sin x)$
I know that $f(3x^2)$ is the same that we say $g = 3x^2$ so it's domain is $R$
When we have $f$ and $g$ functions we can find simply the domain of $fog$ using function composition but how should we find the domain of $fog$ when we don't have $g$ function?
sorry for my bad English
Guide:
We need the following conditions $$3x^2 \in [0,1], 1-x \in [0,1], \sin x \in [0,1].$$
respetively since the output of $g$ needs to be a subset of domain of $f$.