Chapter 7: Transcendental Functions - Section 7.1 - Inverse Functions and Their Derivatives - Exercises 7.1 - Page 373: 23

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

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