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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I already have the answer to this question. But can it be solved interchanging x and y and solving for y.
Please see attached and if possible show solve #25 by interchanging x and y and solving for y.
Thank you.
![25. f (x) =
x+3
x+7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fe49cee-acc8-403b-8d12-20ec3514f583%2Fe480ed8c-59c1-4911-a194-315c2b3b23e1%2Fljfqg3u_processed.png&w=3840&q=75)
Transcribed Image Text:25. f (x) =
x+3
x+7
![Explanation of Solution
Given information:
x+3
Given, function is f (x) =
X+7
Calculation:
The inverse of the function, f (x) = yis given by f-' (y) = x
To find the inverse of the function, the function is set for y and then
solved for x.
X+3
X+7
Multiplying x + 7on both sides,
r + 7) = y (x+ 7)
X+7
x+3 = xy + 7y
Subtracting xy and 3 on both sides,
х+3— ху— 3 — ху + Ту— ху — 3
х — ху — Ту — 3
Factoring x,
x (1- у) — Ту — 3
Dividing by 1-y on both sides,
x(1-y)
1-y
Ту-3
1-y
7y-3
x =
1-y
Hence the inverse is given by f-l (y) =
7y-3
1-y
Therefore, the inverse of the function is f-l (x) =
7x-3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fe49cee-acc8-403b-8d12-20ec3514f583%2Fe480ed8c-59c1-4911-a194-315c2b3b23e1%2Fyc5qsn_processed.png&w=3840&q=75)
Transcribed Image Text:Explanation of Solution
Given information:
x+3
Given, function is f (x) =
X+7
Calculation:
The inverse of the function, f (x) = yis given by f-' (y) = x
To find the inverse of the function, the function is set for y and then
solved for x.
X+3
X+7
Multiplying x + 7on both sides,
r + 7) = y (x+ 7)
X+7
x+3 = xy + 7y
Subtracting xy and 3 on both sides,
х+3— ху— 3 — ху + Ту— ху — 3
х — ху — Ту — 3
Factoring x,
x (1- у) — Ту — 3
Dividing by 1-y on both sides,
x(1-y)
1-y
Ту-3
1-y
7y-3
x =
1-y
Hence the inverse is given by f-l (y) =
7y-3
1-y
Therefore, the inverse of the function is f-l (x) =
7x-3
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