[SOLVED] Domain of composite of inverse

Hi all,

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

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

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

$\displaystyle

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

$

be two invertible functions , then the what is the domain of $\displaystyle

f^{-1}(g^{-1}(x))

$

(Thinking)

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

Is it correct?

I have got it correctly , checked the answer booklet:D

Thanks to all,

Adarsh