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Chapter 12: Q 24. (page 916)

In Exercise, evaluate the given function at the specified points in the domain, and then find the domain and range of the function.

gx,y=x2+y2x+y,蟺,1,4,5

Short Answer

Expert verified

f(蟺,1)=蟺2+1蟺+1f(4,5)=419

Domain is R2-x,y|x+y=0:x,y鈭�R.

Range is R.

Step by step solution

01

Step 1. Given information

Function isgx,y=x2+y2x+y

02

Step 2. Explanation

f(蟺,1)=(蟺)2+(1)2蟺+1=蟺2+1蟺+1f(4,5)=(4)2+(5)24+5=16+259=419

For domain:

x+y=0x=-y

As a result, the points on the line x + y = 0 must be eliminated from the function's domain. There are no limitations on the output values.

So, domain of the given function is鈩�2-{(x,y)鈭�x+y=0;x,y鈭�鈩�}while as the range of function is R.

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