00:01
For this problem, we are asked to describe the domain and range of the function f of x, y, z equals x times y plus z, times e to the power of z over x.
00:10
Now, to begin, let's look at the domain.
00:13
Now, we have some multiplication, we have a square root, and we have exponentiation with division.
00:17
So this square root, we know that a square root has to have argument that is greater than or equal to zero.
00:24
So we get that y plus z must be greater than or equal to zero, or that y must be greater than or equal to zero, or equal to negative z.
00:33
We also have that, because of this e to the power of z over x, we have that x cannot equal zero because of the division.
00:43
So we can say that it's going to be, or that the domain is going to be the real numbers such that y is greater than negative z and x does not equal zero...