BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 2, Problem 3T

(a)

To determine

To find: The formula that expresses f algebraically.

Expert Solution

Answer to Problem 3T

The formula that expresses f algebraically is f(x)=(x2)3 .

Explanation of Solution

The given description is that “subtract 2, then cube the result”,

Let the function bex,

f(x)=x

Subtract 2 from the function.

f(x)=x2

Cube the result of the above function.

f(x)=(x2)3

Hence, the formula that expresses f algebraically is f(x)=(x2)3 .

(b)

To determine

To find: The values of f at the given inputs.

Expert Solution

Answer to Problem 3T

The formula that expresses f algebraically is f(x)=(x2)3 .

Explanation of Solution

Given:

The given inputs are 1 , 0, 1, 2, 3 and 4.

Calculations:

From part (a) the formula is,

f(x)=(x2)3

Substitute 1 for x in the above formula to calculate the value of f(1) ,

f(1)=(12)3=(3)3=27

The value of f(x) at 1 is 27 .

Substitute 0 for x in the above formula to calculate the value of f(0) ,

f(0)=(02)3=(2)3=8

The value of f(x) at 0 is 8 .

Substitute 1 for x in the above formula to calculate the value of f(1) ,

f(1)=(12)3=(1)3=1

The value of f(x) at 1 is 1 .

Substitute 2 for x in the above formula to calculate the value of f(2) ,

f(2)=(22)3=(0)3=0

The value of f(x) at 2 is 0.

Substitute 3 for x in the above formula to calculate the value of f(3) ,

f(3)=(32)3=(1)3=1

The value of f(x) at 3 is 1 .

Substitute 4 for x in the above formula to calculate the value of f(4) ,

f(4)=(42)3=(2)3=8

The value of f(x) at 4 is 8 .

The value of f(x) at 1 is 27 , f(x) at 0 is 8 , f(x) at 1 is 1 , f(x) at 2 is 0, f(x) at 3 is 1 and f(x) at 4 is 8 .

Write all the value in the table,

x y
1 27
0 8
1 1
2 0
3 1
4 8

(c)

To determine

To sketch:  The graph of f using the table values of part (b).

Expert Solution

Explanation of Solution

From the part (b) plot all the points and connect the points to make a smooth curve.

The graph of f is shown in Figure (1),

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2, Problem 3T

Figure (1)

Thus, Figure (1) shows the graph of function.

(d)

To determine

To explain: The f has inverse and verbal description for f1 .

Expert Solution

Answer to Problem 3T

Inverse can check by horizontal line test and verbal description for f1 is “take cube root and then add 2”.

Explanation of Solution

Check by horizontal line test,

The given function is,

f=(x2)3

Take cube root of both side,

f1/3=(x2)

Add 2 on both side,

f1/3+2=xx=2+f1/3f1=x=2+f1/3

So, the inverse of f is 2+f1/3 .

Inverse can check by horizontal line test and verbal description for f1 is “take cube root and then add 2”.

(e)

To determine

To find: The formula for algebraic expression of f1 .

Expert Solution

Answer to Problem 3T

The inverse of f is f1/3+2 .

Explanation of Solution

From part (a) the function is,

f=(x2)3

Take cube root on both side of the function,

f1/3=(x2)

Add 2 on both sides of the function,

f1/3+2=xf1=x=f1/3+2f1=f1/3+2

Hence, the inverse of f is f1/3+2 .

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