Answer
Let $g(x, y) = cos(x+2y)$
a) Evaluate $g(2, -1)$
$cos(0)=1$
b) Find the domain of $g$
$D=\{(x, y) | x+2y\geq 0\}$
c) Find the range of $g$
$R=\{f(x, y) | cos(x+2y)\in D\}$
or
$R=\{z|z=cos(x+2y) \in D\}$
Work Step by Step
a) Evaluate $g(2, -1)$
Input the given values of $g(x, y)$ into the function $cos(x+2y)$.
$cos((2)+2(-1))$
=> $cos(0)=1$
b) Find the domain of $g$
In this case, the domain of this function is the element $(x+2y)$
$D=\{(x, y) | x+2y\geq 0\}$
c) Find the range of $g$
Let $f(x, y) = z$, the range of this function is the entire function.
$R=\{f(x, y) | cos(x+2y)\in D\}$
or
$R=\{z|z=cos(x+2y) \in D\}$
