How would you use part a to find out part b? **Title: Understanding Inverse Functions Using Graphical Analysis**This educational resource explores the concept of inverse functions through graphical representation. Follow the steps below to learn how to sketch and analyze inverse functions:### Task:Use the graph of \( y = f(x) \) in (Figure 1 and Figure 2) to evaluate the following:#### (a) Sketch the graph of \( y = f^{-1}(x) \)- **Equation:** \(\frac{1 - (-3)}{2 - 0} = \frac{4}{2} = 2\)- **Derivation:** - Rewrite as \( y = \frac{x + 3}{2} \) - Thus, \( f^{-1}(x) = \frac{x + 3}{2} \)- **Graph Explanation:** Two graphs are shown: 1. **Left Graph:** This is a linear graph depicting the function \( f^{-1}(x) \) passing through points (-3, 0) and (0, 1). This represents the line \( y = \frac{x + 3}{2} \), illustrating the inverse function. 2. **Right Graph:** This graph includes both \( f(x) \) and \( f^{-1}(x) \), indicating their relationship and symmetry about the line \( y = x \).#### (b) Use part (a) to estimate \( f^{-1}(1) \)- To estimate \( f^{-1}(1) \), observe the positions where the inverse graph intersects with \( y = 1 \).These exercises demonstrate how to visualize and understand the functionalities and calculations related to inverse functions, essential for mathematical proficiency. ### Graph Analysis for Educational Website#### Figure 1: Graph of \( y = f(x) \)The first graph depicts a linear function passing through the origin and extending from the third quadrant to the first quadrant. The line increases steadily with a positive slope, indicating a direct proportional relationship between \( x \) and \( y \). - **X-Axis**: Extends from -4 to 4.- **Y-Axis**: Extends from -4 to 4.- **Key Characteristics**: - The line crosses the y-axis at (0,0). - The slope is positive, indicating an increasing function.#### Figure 2: Graph of \( y = f(x) \)The second graph illustrates a logarithmic curve, which appears to flatten out as \( x \) increases. It shows typical behavior of logarithmic growth:- **X-Axis**: Extends from -4 to 4.- **Y-Axis**: Extends from -4 to 4.- **Key Characteristics**: - The curve commences from the left and transitions from the third quadrant, gradually approaching the x-axis but never actually reaching negative values on the x-axis. - The curve flattens as it moves to the right, indicative of slower rates of increase as \( x \) becomes larger.These graphs provide insight into different types of mathematical functions, demonstrating linear vs. logarithmic relationships.

Answered: Use the graph of f (x) in (Figure 1 and…

Use the graph of f (x) in (Figure 1 and Figure 2) to evaluate the following: |-(-3) 4 (a) Sketch the graph of y = f-(x) 2 2 - 0 X43 ye tx().す - 2 =メ f (x) -3 (b) Use part a to estimate f-'(1)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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What about b and C?
Part (iv) of the question please
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