6.7 Inverse Relations and Functions p405. Ex) Find the inverse.

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6.7 Inverse Relations and Functions p405

Ex) Find the inverse.

Notice… the domain of the relation is now the range of the inverse. The range of the relation is now the domain of the inverse.

Ex) Find the equation for the inverse of the Relation described by What are the graphs of the relation and its inverse?

Ex) Find the domain and range of the relation. Then determine if it is a function. Find the domain and range of the inverse and determine if it is a function. Graph the relation and the inverse.

In real-world applications, the dependence of variables is fixed, so their order should NOT be switched when finding inverses. We use the same equation, “expressed inversely”. In other words, simply solve for the required variable, but DO NOT switch them.

Ex) The function d=4.9t 2 represents the distance d, in meters, that an object falls in t seconds due to Earth’s gravity. Find the inverse of this function.

If and are inverse functions, then and for x in the domains of and respectively.

Ex) For, find, and