Chapter 12.1, Exercise 7

Problem

Give the domain and range of the multivariable function:

\[f(x,y)=x^2+y^2+2\]

Solution:

\[0≤x^2+y^2+2\]

\[−2≤x^2+y^2\]

\[x^2+y^2≥−2\]

\[D:{(x,y):x^2+y^2≥−2}\]

\[Domain: D:{(x,y):x^2+y^2≥−2}\]

\[f(0,0):0^2+0^2+2\]

\[f(0,0):0+0+2\]

\[f(0,0):2\]

\[R:{(x,y):[2,∞]}\]

\[Range: R:{(x,y):[2,∞]}\]