Intermediate Algebra
19th Edition
ISBN: 9780998625720
Author: Lynn Marecek
Publisher: OpenStax College
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
Question
![### 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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Explain how the graph of the inverse of a function is related to the graph of the function.arrow_forwardCan a function be its own inverse? Explain.arrow_forwardIf the order is reversed when composing two functions, can the result ever be the same as the answer in the original order of the composition? If yes, give an example. If no, explain why not.arrow_forward
- During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6 hours, and at a rate of 0.5 inch per hour for the final hour. Write and graph a piecewise-defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?arrow_forwardWhen examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift?arrow_forwardHow do you find the domain for the composition of two functions, fg ?arrow_forward
- When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the x-axis from a reflection with respect to the y-axis?arrow_forwardUse f (x) = x – 3 and g (x) = to find the x+3 given functions. (2 points each) 1) g • f 2) g • g Find the inverse of f. (3 points each) 4х-3 3) f (x) = 1-8х 4) f (x) = 2 Submit Assignment ( Previous Next 000 000 Dashboard Calendar To Do Notifications Inboxarrow_forwardConsider the function. (x) = 2x - 1 (a) Find the inverse function of f. f-x) = (b) Graph f and fon the same set of coordinate axes. Graph Layers After you add an you can use Grap and edit its proper 12 -2 -2 No Solution Help Till WebAssign. Graphing Tool (c) Describe the relationship between the graphs. The graphs of f and f - are reflections of each other across the line y = (d) State the domain and range of f and f -. (Enter your answers using interval notation.) domain off range of f domain of f range of f-arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning