Question

Let g(x, y) = cos(x + 5y). (a) Evaluate g(10, −2). g(10, −2) = (b) Find the domain of g. −1 ≤ x ≤ 1, − 1 5 ≤ y ≤ 1 5 −5 ≤ x ≤ 5, −1 ≤ y ≤ 1 −1 ≤ x + 5y ≤ 1 the set of real numbers2 − π 2 ≤ x + 5y ≤ π 2 (c) Find the range of g. (Enter your answer using interval notation.)

Answer 1

Answer:

since $Cos(z)$ is a function defined for all $z\in \mathbb{R}$, then there is not restriction for $x+5y$, thus, the domain of $g(x,y)$ is $\mathbb{R}^2$ and in interval notation is $(-\infty,\infty)\times(-\infty,\infty)$

Since $Cos(x+5y)\in\mathbb{R}$ then the range of $g(x,y)$ is the interval [-1,1].