Intermediate Algebra
19th Edition
ISBN: 9780998625720
Author: Lynn Marecek
Publisher: OpenStax College
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![### Inverse Function Calculation Example
Consider the function defined as follows:
\[ f(x) = 2x + 14 \]
We are tasked with finding the inverse of this function, denoted by \( f^{-1}(x) \). In order to find the inverse, we need to perform the following steps:
1. **Start with the original equation:**
\[ y = 2x + 14 \]
2. **Swap \( x \) and \( y \) to begin solving for the inverse:**
\[ x = 2y + 14 \]
3. **Solve this new equation for \( y \):**
\[ x - 14 = 2y \]
\[ y = \frac{x - 14}{2} \]
Thus, the inverse function is:
\[ f^{-1}(x) = \frac{x - 14}{2} \]
#### Input Field for Verification
You may input the calculated inverse function in the provided input field and use the "Preview" button to verify your answer.
\[ f^{-1}(x) = \ \boxed{\ \ \ \ \ \ \ \ \ \ } \]
<button disabled>Preview</button>
By following these steps, you can find the inverse function for any given linear function. This process helps to understand the relationship between the original function and its inverse, which essentially reverses the effect of the original function.](https://content.bartleby.com/qna-images/question/244f2dd3-56b0-4e55-8cec-63e02ab2a541/f8599e45-c4b4-4b9b-bb15-f1c1bbc83adf/j88vfw7.png)
Transcribed Image Text:### Inverse Function Calculation Example
Consider the function defined as follows:
\[ f(x) = 2x + 14 \]
We are tasked with finding the inverse of this function, denoted by \( f^{-1}(x) \). In order to find the inverse, we need to perform the following steps:
1. **Start with the original equation:**
\[ y = 2x + 14 \]
2. **Swap \( x \) and \( y \) to begin solving for the inverse:**
\[ x = 2y + 14 \]
3. **Solve this new equation for \( y \):**
\[ x - 14 = 2y \]
\[ y = \frac{x - 14}{2} \]
Thus, the inverse function is:
\[ f^{-1}(x) = \frac{x - 14}{2} \]
#### Input Field for Verification
You may input the calculated inverse function in the provided input field and use the "Preview" button to verify your answer.
\[ f^{-1}(x) = \ \boxed{\ \ \ \ \ \ \ \ \ \ } \]
<button disabled>Preview</button>
By following these steps, you can find the inverse function for any given linear function. This process helps to understand the relationship between the original function and its inverse, which essentially reverses the effect of the original function.
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