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Chapter 2: Problem 81

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=|x-2| $$

Short Answer

Expert verified
The function f(x) = |x-2| is not a one-to-one function because it fails the horizontal line test. Therefore, the function does not have an inverse that is also a function.

Step by step solution

01

Graphing the function

Using a graphing utility, graph the function f(x) = |x-2|. This function gives the absolute value of (x-2), which means it will be a V-shaped graph with its vertex at the point (2,0).
02

Testing for one-to-one

To determine whether the function f(x) = |x-2| is one-to-one, apply the horizontal line test. Draw horizontal lines across the graph. If any horizontal line intersects the graph at more than one point, the function is not one-to-one. Based on the graph from Step 1, it is seen that the function is not one-to-one because many horizontal lines intersect the graph at two points.

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