Answer
a. $g\left(2,-1\right)=cos\left(2+2\left(-1\right)\right)=cos\left(0\right)=1$
b. $D=\left\{g\in \mathbb{R}^2\right\}$
c. $\left[-1,1\right]$
Work Step by Step
a. Evaluate: $g\left(2,-1\right)=cos\left(2+2\left(-1\right)\right)=cos\left(0\right)=1$
b. Since cosine is defined for all real numbers, $g\left(x,y\right)$ is defined for all real values of x,y. Domain of $g$ is $D=\left\{g\in \mathbb{R}^2\right\}$
c. The cosine function from $\mathbb{R}$ to $\mathbb{R}$ has range $\left[-1,1\right]$. Any value in $\mathbb{R}$ can be attained as $x+2y$ for some $(x,y)\in\mathbb{R}^2$. Thus the range of $g$ is the same: $\left[-1,1\right]$.
