### Inverse Function Calculation ExampleConsider 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 VerificationYou may input the calculated inverse function in the provided input field and use the "Preview" button to verify your answer.\[ f^{-1}(x) = \ \boxed{\ \ \ \ \ \ \ \ \ \ } \]PreviewBy 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.

To find f-1(x) Step 1- put f(x) equals to y Step 2 - Replace y with x and x with y Step 3-…

Answered: Let f(x) :2x + 14 f-'(x) = Prev

Math

Calculus

Let f(x) :2x + 14 f-'(x) = Prev

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Functions And Their Graphs

Section2.4: A Library Of Parent Functions

Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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.

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Consider 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-