### Problem Statement**(L4) 10.** Given the function $ f(x) = \sqrt{x - 4} $ has an inverse, find $ f^{-1}(x) $. Then, ACCURATELY graph $ f(x) $, $ f^{-1}(x) $, and $ f \circ f^{-1}(x) $ on the same set of axes. Explain the relationship between the graph of $ f \circ f^{-1}(x) $ and the individual functions of $ f(x) $ and $ f^{-1}(x) $.### Graph DescriptionThe graph provided is a coordinate plane with both x and y axes ranging from -6 to 6. It is divided into grid squares, each representing one unit on both axes. The function $ f(x) $, its inverse $ f^{-1}(x) $, and their composition $ f \circ f^{-1}(x) $ should be plotted on this graph.### Explanation______________________________________________________________________________________________________________________________________________________

Given: f(x)=x-4. To Find: fx, f-1x and fof-1x

Answered: Given the function f(x) = Vx – 4 has an…

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...

See similar textbooks

Related questions

Concept explainers

Question

### Problem Statement

**(L4) 10.** Given the function $ f(x) = \sqrt{x - 4} $ has an inverse, find $ f^{-1}(x) $. Then, ACCURATELY graph $ f(x) $, $ f^{-1}(x) $, and $ f \circ f^{-1}(x) $ on the same set of axes. Explain the relationship between the graph of $ f \circ f^{-1}(x) $ and the individual functions of $ f(x) $ and $ f^{-1}(x) $.

### Graph Description

The graph provided is a coordinate plane with both x and y axes ranging from -6 to 6. It is divided into grid squares, each representing one unit on both axes. The function $ f(x) $, its inverse $ f^{-1}(x) $, and their composition $ f \circ f^{-1}(x) $ should be plotted on this graph.

### Explanation

__________________________________________________

__________________________________________________

__________________________________________________

Expert Solution

Step 1

Given:

$f (x) = \sqrt{x - 4 .}$

To Find:

$f (x), f^{- 1} (x) and f o f^{- 1} (x)$

Step 2

Explanation:

$Firstly, we will find f^{- 1} (x), and f o f^{- 1} (x) . Let y = f (x) = \sqrt{x - 4} \Rightarrow y = \sqrt{x - 4} \Rightarrow y^{2} = x - 4 \Rightarrow x = y^{2} + 4 now, interchanging the variables, we get: y = x^{2} + 4 Hence, f^{- 1} (x) = x^{2} + 4 .$

$Now, we will find f o f^{- 1} (x) f o f^{- 1} (x) = f [f^{- 1} (x)] = \sqrt{[f^{- 1} (x)] - 4} = \sqrt{x^{2} + 4 - 4} = \sqrt{x^{2}} = |x| \Rightarrow f o f^{- 1} (x) = |x| .$

Step 3

Step by step

Solved in 5 steps with 1 images

Knowledge Booster

$Limits and Continuity$

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