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

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)*(-\infty,\infty)`

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