Notes 6­6 Functions and Their Inverses
Objectives:
­ Determine whether the inverse of a function is a function
­ Write rules for the inverses of functions. Who uses this?
Nurses can use inverse functions to approximate the ages of infants. 1
Previously, you learned that the inverse function of a function "undoes" f(x). Its graph is a reflection across the line y = x. The inverse may or may not be a function...
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Ex. Use the horizontal­line test to determine whether the inverse of each relation is a function.
a. blue relation
b. red relation
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Ex. Find the inverse of state the its domain and range
. Determine whether it is a function, and 4
Try These:
Ex. Find the inverse of its domain and range.
. Determine whether it is a function, and state 5
Not all inverses of functions are not necessarily functions. When both a relation and its inverse are functions, the relation is called one­to­one function.
In a one­to­one, each y­value is paired with exactly one x­value.
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Ex. Determine by composition whether each pair of functions are inverses.
a. and
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b. For x ≥ 0, and
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Try These:
Ex. Determine by composition whether each pair of functions are inverses
a.
and
b. and
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