Carroll Gray
06/15/2024 · Junior High School
If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." \( \{(6,-7),(11,-6),(9,-5),(7,-4)\} \)
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Step-by-step Solution
To determine if the function defined by the set of ordered pairs \(\{(6,-7),(11,-6),(9,-5),(7,-4)\}\) is one-to-one, we need to check if each output (the second element of each pair) is unique.
The outputs from the pairs are:
- For \(6\), the output is \(-7\).
- For \(11\), the output is \(-6\).
- For \(9\), the output is \(-5\).
- For \(7\), the output is \(-4\).
All outputs \(-7\), \(-6\), \(-5\), and \(-4\) are unique. Since no two different inputs produce the same output, the function is indeed one-to-one.
Now, to find the inverse of the function, we will switch the roles of the inputs and outputs in each ordered pair. The inverse will be:
\[
\{(-7, 6), (-6, 11), (-5, 9), (-4, 7)\}
\]
Thus, the inverse of the function is:
\[
\{(-7, 6), (-6, 11), (-5, 9), (-4, 7)\}
\]
Quick Answer
The function is one-to-one and its inverse is \(\{(-7, 6), (-6, 11), (-5, 9), (-4, 7)\}\).
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