Sketch the graph of the inverse of the function graphed...

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Key Concepts

Graphical Reflection

Graphing the inverse function is achieved by reflecting the graph of the original function across the line y = x. This reflection flips the coordinates of every point (x, y) to (y, x) and provides a visual representation of how the inverse function relates to the original function.

Inverse Function

An inverse function reverses the roles of inputs and outputs of a given function. If a function f maps an element x to y, then its inverse, denoted as f?¹, maps y back to x. This concept is fundamental in algebra and calculus and is used in solving equations where the variable needs to be isolated.

Domain and Range Exchange

For an inverse function, the domain and range of the original function are interchanged. Specifically, the domain of the original function becomes the range of its inverse, and the range of the original function becomes the domain of the inverse. This interchange is critical when determining the valid inputs and outputs after inverting a function.

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