Chapter 7: Transcendental Functions - Section 7.1 - Inverse Functions and Their Derivatives - Exercises 7.1 - Page 373: 22

$$ f^{-1}(x)=\sqrt{x}+1 $$

Given $$ y=x^{2}-2x+1$$ Find the inverse: \begin{aligned} & y=x^{2}-2x+1\\ & y=(x - 1)^2\\ & \Rightarrow x-1=\sqrt y \\ &\Rightarrow x=\sqrt y+1, \\ &\text{Switch $ x $ and $ y $}\\ &y=\sqrt{x}+1=f^{-1}(x) \end{aligned}