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 2.7, Problem 3E

(a)

To determine

To write: A verbal description of inverse function f1 .

Expert Solution

Answer to Problem 3E

The verbal description of inverse function of f is Take the cube root, subtract 5, and then divide the result by 3.

Explanation of Solution

Given:

The function f is given which element is multiplied by 3 and added 5 and taken the third power of the whole result.

Calculation:

The verbal description gives the value of f is,

f(x)=(3x+5)3 (1)

Let f(x) is assumed to be equal to y,

So, the function f(x) becomes,

y=f(x)

Substitute y for f(x) in equation (1), and find the value of x,

y=(3x+5)3y13=3x+5y135=3xy1353=x

Interchange the x and y in above equation,

y=x1353

The above equation is an inverse function of f(x) ,

f1(x)=x1353

Thus, the verbal description of inverse function of f is Take the cube root, subtract 5, and then divide the result by 3.

(b)

To determine

To find: The algebraic formulas of function f and f1 in terms of input x.

Expert Solution

Answer to Problem 3E

The function of f is, f(x)=(3x+5)3 and the function of f1 is f1(x)=x1353 .

Explanation of Solution

Given:

The function f is given which element is multiplied by 3 and added 5 and taken the third power of the whole result.

Calculation:

The verbal description is given in part (a),

The algebraic formula of function f is in terms of x is,

f(x)=(3x+5)3

From part (a) the inverse function of function f(x) has verbal description , which is, Take the cube root, subtract 5, and then divide the result by 3.

From above verbal description the algebraic formula of function f1 is f1(x)=x1353 .

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