5. (3 pts) Find a formula for the inverse function ƒ¯¹(x) if f(x)=- Solution 1 Write y=- where x = dom(f). 2x+3 4x-1 Step 1: Solve for x in terms of y: 2x+3 4x-1 2x+3 y= 4x-1 >> 4xy-y=2x+3 4xy-2x-3+y (0, 1, 2) 2x(2y-1)=3+y ⇒ x=- 3+y 2(2y-1) with (y #1/2). Step 2: Interchange x and y: y 3+x 2(2x-1) with x=1/2 Therefore, the formula for the inverse function of f is given by: f(x)= (0, 0.5,1) 3+x 2(2x-1) Solution 2 Write y=- where x = dom(f). 2x+3 4x-1 Step 1: Interchange x and y: x=. 2y+3 4y-1 with (y =1/4)" Step 2: Solve for y in terms of x: 2y+3 x=- 4y-1 4xy-x-2y+3 ⇒ 4xy-2y=3+x (0,1,2) 2y(2x-1)=3+xy= 3+x 2(2x-1) with (x=1/2). (0, 0.5,1) Therefore, the formula for the inverse function of ƒ is given by: f(x)=- 3+x 2(2x-1)
5. (3 pts) Find a formula for the inverse function ƒ¯¹(x) if f(x)=- Solution 1 Write y=- where x = dom(f). 2x+3 4x-1 Step 1: Solve for x in terms of y: 2x+3 4x-1 2x+3 y= 4x-1 >> 4xy-y=2x+3 4xy-2x-3+y (0, 1, 2) 2x(2y-1)=3+y ⇒ x=- 3+y 2(2y-1) with (y #1/2). Step 2: Interchange x and y: y 3+x 2(2x-1) with x=1/2 Therefore, the formula for the inverse function of f is given by: f(x)= (0, 0.5,1) 3+x 2(2x-1) Solution 2 Write y=- where x = dom(f). 2x+3 4x-1 Step 1: Interchange x and y: x=. 2y+3 4y-1 with (y =1/4)" Step 2: Solve for y in terms of x: 2y+3 x=- 4y-1 4xy-x-2y+3 ⇒ 4xy-2y=3+x (0,1,2) 2y(2x-1)=3+xy= 3+x 2(2x-1) with (x=1/2). (0, 0.5,1) Therefore, the formula for the inverse function of ƒ is given by: f(x)=- 3+x 2(2x-1)
ChapterP: Prerequisites
SectionP.4: Factoring Polynomials
Problem 84E: The rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the...
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Can you show the steps of how to get this answer, and explain all the steps.
![5. (3 pts) Find a formula for the inverse function ƒ¯¹(x) if f(x)=-
Solution 1 Write y=- where x = dom(f).
2x+3
4x-1
Step 1: Solve for x in terms of y:
2x+3
4x-1
2x+3
y=
4x-1
>> 4xy-y=2x+3
4xy-2x-3+y
(0, 1, 2)
2x(2y-1)=3+y ⇒ x=-
3+y
2(2y-1)
with (y #1/2).
Step 2: Interchange x and y: y
3+x
2(2x-1)
with x=1/2
Therefore, the formula for the inverse function of f is given by: f(x)=
(0, 0.5,1)
3+x
2(2x-1)
Solution 2 Write y=- where x = dom(f).
2x+3
4x-1
Step 1: Interchange x and y: x=.
2y+3
4y-1
with (y =1/4)"
Step 2: Solve for y in terms of x:
2y+3
x=-
4y-1
4xy-x-2y+3 ⇒ 4xy-2y=3+x
(0,1,2)
2y(2x-1)=3+xy=
3+x
2(2x-1)
with (x=1/2).
(0, 0.5,1)
Therefore, the formula for the inverse function of ƒ is given by: f(x)=-
3+x
2(2x-1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6356ceb6-8738-457b-86a1-1decb02218d2%2Faff5e913-9f86-4c31-8fed-04f9a273659a%2Fr7w41yo_processed.png&w=3840&q=75)
Transcribed Image Text:5. (3 pts) Find a formula for the inverse function ƒ¯¹(x) if f(x)=-
Solution 1 Write y=- where x = dom(f).
2x+3
4x-1
Step 1: Solve for x in terms of y:
2x+3
4x-1
2x+3
y=
4x-1
>> 4xy-y=2x+3
4xy-2x-3+y
(0, 1, 2)
2x(2y-1)=3+y ⇒ x=-
3+y
2(2y-1)
with (y #1/2).
Step 2: Interchange x and y: y
3+x
2(2x-1)
with x=1/2
Therefore, the formula for the inverse function of f is given by: f(x)=
(0, 0.5,1)
3+x
2(2x-1)
Solution 2 Write y=- where x = dom(f).
2x+3
4x-1
Step 1: Interchange x and y: x=.
2y+3
4y-1
with (y =1/4)"
Step 2: Solve for y in terms of x:
2y+3
x=-
4y-1
4xy-x-2y+3 ⇒ 4xy-2y=3+x
(0,1,2)
2y(2x-1)=3+xy=
3+x
2(2x-1)
with (x=1/2).
(0, 0.5,1)
Therefore, the formula for the inverse function of ƒ is given by: f(x)=-
3+x
2(2x-1)
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