Find the domain of the following function h(x,y) = sqrt(x-9y+5)?

To find the domain of the function h(x, y) = sqrt(x - 9y + 5), we need to determine the values of x and y for which the function is defined.

1. Square root function: Remember that the square root of a number is only defined for non-negative real numbers. Therefore, the expression inside the square root, (x - 9y + 5), must be greater than or equal to zero.

x - 9y + 5 ≥ 0
x - 9y ≥ -5
x ≥ 9y - 5

2. The domain of the function will be determined by the values of x and y that satisfy the inequality x ≥ 9y - 5.

In general, unless further restrictions are given, the domain of a function h(x, y) usually includes all real numbers. However, if there are additional constraints or specific ranges provided for x and y, those constraints should be considered.

Therefore, the domain of the function h(x, y) = sqrt(x - 9y + 5) is x ≥ 9y - 5.

To find the domain of the function h(x, y) = sqrt(x - 9y + 5), we need to determine the values of x and y for which the function is defined.

In this case, the function h(x, y) is defined as long as the expression inside the square root is nonnegative (greater than or equal to 0). Therefore, we need to consider the inequality:

x - 9y + 5 ≥ 0

To solve this inequality, we isolate the variable x:

x ≥ 9y - 5

Now we have the condition for x in terms of y. Therefore, the domain of the function h(x, y) is all the values of (x, y) that satisfy the inequality x ≥ 9y - 5.

In summary, the domain of the function h(x, y) = sqrt(x - 9y + 5) is given by the inequality x ≥ 9y - 5.

Since sqrt(x) requires x≥0, therefore the domain of the function is such that:

x-9y+5≥0
equivalently:
9y≤x+5
or
dom h(x,y) = {x,y ∈ℝ | 9y≤x+5}