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 10T

(a)

To determine

To find: The inverse of the function f(x)=3x

Expert Solution

Answer to Problem 10T

The inverse f1 of given function is 3x2.

Explanation of Solution

Given:

The function is, f(x)=3x

Calculation:

Rewrite the function as y=3x (1)

The above equation is defining y as a function of x.

Square equation (1) and simplify as follows,

(y)2=(3x)2y2=3x

Isolate x on one side of the equation.

x=3y2

Interchange the variables x and y in above equation.

y=3x2

Thus, the inverse f1 of given function is 3x2.

(b)

To determine

To sketch: The graph of f(x)=3x and its inverse on same coordinate axes.

Expert Solution

Explanation of Solution

Use transformation and first sketch the graph of f(x)=3x

Sketch graph of x and take its reflection about y-axis and then move it right on horizontal axis by 3 units.

To sketch the graph of f1=3x2 take reflection of graph of f(x) and reflect it in the line y=x.

Sketch graph of f(x) and f1(x) as shown below.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2, Problem 10T

From the above Figure, it can be observed that f1(x) is a reflection f(x) in y=x.

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