山TOof CGiven the function f(x) = Vx – 4 has an inverse, find f-1(x). Then, ACCURATELYgraph f(x), f-1(x) and fof-1(x) on the same set of axis. Explain the relationshipbetween the graph of fof-1(x) and the individual functions of f (x) and f-1(x).(L4) 10.f(x).5--4..3-一5 5 4 山七4 5-3.-6+-Explanation:3.+,6.

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

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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.7: Inverses Of Linear-functions

Problem 32PPS

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Question

山
TO
of C
Given the function f(x) = Vx – 4 has an inverse, find f-1(x). Then, ACCURATELY
graph f(x), f-1(x) and fof-1(x) on the same set of axis. Explain the relationship
between the graph of fof-1(x) and the individual functions of f (x) and f-1(x).
(L4) 10.
f(x)
.5-
-4.
.3-
一5 5 4 山七
4 5
-3.
-6+-
Explanation:
3.
+,
6.

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

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