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Chapter 2: Q. 34 (page 69)

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

x+y2=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.

x+y2=1

02

Step 2. The given equation is x+y2=1

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

Subtract xon both side

x+y2-x=1-xy2=1-x

taking square root on both side

y2=1-xy=卤1-x

03

Step 3. For example, if x=0

y=卤1-0y=卤1y=卤1

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

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