The inverse of the function simply reversing the operation.

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.7, Problem 91E

a.

To determine

To find: The inverse of the function simply reversing the operation.

Expert Solution

f1(x)=5x12

Explanation of Solution

Given information: f(x)=(2x+1)5

Concept used: To find the inverse of a function; we simply reverse the operation.

Calculation:

f(x)=(2x+1)5

Here, the operation is “Multiply by 2 , add 1 then divide by 5 ”.

So, the reverse of the operation “Multiply by 2 , add 1 then divide by 5 ” is “Multiply by 5 , subtract 1 then divide by 2 ”.

Therefore, f1(x)=5x12

b.

To determine

Expert Solution

f1(x)=13x

Explanation of Solution

Given information: f(x)=31x

Concept Used: To find the inverse of a function; we simply reverse the operation.

Calculation:

f(x)=31x

Here, the operation is “Take reciprocal, multiply by (1) then add 3

So, the reverse of the operation “Take reciprocal, multiply by (1) then add 3 ” is “Subtract 3 , divide by (1) then take reciprocal” .

Therefore, f1(x)=13x

c.

To determine

Expert Solution

f1(x)=x223

Explanation of Solution

Given information: f(x)=x3+2

Concept used: To find the inverse of a function; we simply reverse the operation

Calculation:

Here, the operation is, “First cube, add 2 then square root”

So, the reverse of the operation is “First square, subtract 2 then cube root”.

Therefore, f1(x)=x223

d.

To determine

To find: The inverse of the function simply reversing the operation.

Expert Solution

f1(x)=(x3+5)2

For the function f(x)=x3+2x+6 , it is not possible to find the inverse simply reversing the operation because in this function two terms with x are present; one is x3 another is 2x .

Explanation of Solution

Given information: f(x)=(2x5)3

Concept used: To find the inverse of a function; we simply reverse the operation

Calculation:

Here, the operation is, “Multiply by 2 , subtract 5 then cube ”

So, the reverse of the operation is “First cube root , add 5 then divide by 2 ”.

Therefore, f1(x)=(x3+5)2

Another function is f(x)=x3+2x+6

It is not possible to find the inverse simply reversing the operation because in this function two terms with x are present; one is x3 another is 2x .

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