Question: how to find inverse function of a domain?
Answer: If f ( x ) = ( x − 1 ) 2 \displaystyle f\left(x\right)={\left(x - 1\right)}^{2} f(x)=(x−1)2​ on [1,∞), then the inverse function is f − 1 ( x ) = x + 1 \displaystyle {f}^{-1}\left(x\right)=\sqrt{x}+1 f−1​(x)=√​x​​​+1. The domain of f = range of f−1​ = [1,∞). The domain of f−1​ = range of f = [0,∞).