find and sketch the domain of the function f(x,y)= x/x^2+y^2

Answered

2022-01-19

find and sketch the domain of the function f(x,y)= x/x^2+y^2

Answer & Explanation

xleb123

xleb123

Expert

2022-01-30Added 27 answers

f(x,y)=xx2+y2

Cancel the common factor of x and x2.

Raise x to the power of 1.

f(x,y)=x1x2+y2

Factor x out of x1.

f(x,y)=x1x2+y2

Cancel the common factors.

f(x,y)=1x+y2

Subtract y2 from both sides of the equation.

f(x,y)y2=1x

Set the denominator in 1x equal to 0 to find where the expression is undefined.

x=0

The domain is all values of x that make the expression defined.

Interval Notation:

(,0)(0,)

Set-Builder Notation:

{x|x0}

 

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