# Thread: [SOLVED] Domain of composite of inverse

1. ## [SOLVED] Domain of composite of inverse

Hi all,

Q) $Let f :[2,\infty) \rightarrow [1,\infty)$ defined by

$f(x) = 2 ^{x^4-4x^2}$ and

$g: [\frac{\pi}{2} , \pi] \rightarrow A$ defined by

$
g(x)=\frac{sin(x)+4}{sin(x)-2}
$

be two invertible functions , then the what is the domain of $
f^{-1}(g^{-1}(x))

$

my answer is $[ -5, -\frac{(4+sin(1))}{(2-sin(1))}]$
Is it correct?

I have got it correctly , checked the answer booklet
Thanks to all,