Function Flip WorksheetFunction Flip Investigating Quadratic and Square Root Inverses Name: Date: Instructions Compare and contrast the domain and range of the restricted quadratic function \(f(x)\) and its inverse function \(f^{-1}(x)\). Use interval notation to fill in the table for each problem. 1 \(f(x) = x^2 + 3\),  \(x \ge 0\)  and  \(f^{-1}(x) = \sqrt{x - 3}\) x y 0 10 10 \(f(x)\) \(f^{-1}(x)\) FunctionDomainRange\(f(x)\)\(f^{-1}(x)\) Observational Notes 2 \(f(x) = (x-2)^2\),  \(x \ge 2\)  and  \(f^{-1}(x) = \sqrt{x} + 2\) x y 0 10 10 \(f(x)\) \(f^{-1}(x)\) FunctionDomainRange\(f(x)\)\(f^{-1}(x)\) Observational Notes
Function Flip Answer KeyFunction Flip Key Correct Interval Notation Answers 1 \(f(x) = x^2 + 3\), \(x \ge 0\) Â & Â \(f^{-1}(x) = \sqrt{x - 3}\) FunctionDomainRange\(f(x)\)\([0, \infty)\)\([3, \infty)\)\(f^{-1}(x)\)\([3, \infty)\)\([0, \infty)\) Key Observation Notice the direct swap: The domain of the original becomes the range of the inverse. 2 \(f(x) = (x-2)^2\), \(x \ge 2\) Â & Â \(f^{-1}(x) = \sqrt{x} + 2\) FunctionDomainRange\(f(x)\)\([2, \infty)\)\([0, \infty)\)\(f^{-1}(x)\)\([0, \infty)\)\([2, \infty)\) Key Observation The horizontal shift in the quadratic function becomes a vertical shift in its square root inverse.
