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Chapter 1: Problem 57

use a graphing utility to graph the function. Then use the Horizontal Line Test to determine whether the function is one-to-one. If it is, find its inverse function. $$ f(x)=|x+3| $$

Short Answer

Expert verified
The function \( f(x) = |x + 3| \) is not one-to-one; hence, it does not have an inverse function.

Step by step solution

01

Graphing the Function

Firstly, the function \( f(x) = |x+3| \) is graphed using a graphing utility. This function is an absolute value function, so it will make a V shape graph. The graph will have a vertex at (-3,0).
02

Horizontal Line Test

The Horizontal Line Test means that any horizontal line drawn through the function's graph touches the graph at most one point. However, as it can be observed from the graph, there are horizontal lines that intersect the graph at more than one point. Therefore, the function \( f(x) = |x+3| \) is not one-to-one.
03

Finding the Inverse Function

Since the function is not one-to-one according to the Horizontal Line Test, there is no need to find the inverse function. A function must be one-to-one to have an inverse.

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