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Chapter 2: Q. 37 (page 69)

Determine whether the equation defines y as a function of x.

localid="1645892016772" 2x2+3y2=1

Short Answer

Expert verified

The given equation is not define a function.

Step by step solution

01

Step 1. Given information

In the given question we have to determine whether the equation defines y as a function of x.

2x2+3y2=1

02

Step 2. The given equation is 2x2+3y2=1

To determine whether the given equation is a function, solve the equation for y.

Subtract 2x2on both side

2x2+3y2-2x2=1-2x23y2=1-2x2

03

Step 3. Divide by 3 on both side

33y2=1-2x23y2=1-2x23

Taking square root on both side

y=卤1-2x23

04

Step 3. For example, if x=1

y=卤1-2脳(1)23y=卤1-23y=卤-13

so two different outputs result from the same input. This means that the equation 2x2+3y2=1does not define a function.

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