Name all the values of x that are not in the domain of f(x)=2-x^2/x+5.

Answer: x= -5

2)Find the minimum value of f(x,y)=2x-y+2 for the polygonal convex set determined by this system of inequalities: x >/= 1, x </= 3, y</=0, 1/2x+y</=5

Answer: -0.5

To determine the values of x that are not in the domain of the function f(x) = (2 - x^2) / (x + 5), we need to identify any values of x that would result in an undefined expression.

The function is undefined when the denominator, (x + 5), equals zero, since division by zero is undefined. Therefore, to find the value(s) of x that are not in the domain, we need to solve the equation:

x + 5 = 0

This equation can be solved by subtracting 5 from both sides:

x = -5

Hence, x = -5 is the value that is not in the domain of the function f(x) = (2 - x^2) / (x + 5).

Now, let's determine the minimum value of the function f(x, y) = 2x - y + 2 for the given set of inequalities:

x ≥ 1
x ≤ 3
y ≤ 0
1/2x + y ≤ 5

To find the minimum value, we can analyze the vertices of the polygon formed by the intersection of the given inequalities. The vertices of the polygon can be found by solving the system of equations formed by the equalities of each pair of inequalities.

The vertices are determined by the following equations:

1) When x = 1:
From the first inequality, y can take any value ≤ 0.
From the fourth inequality, y = 5 - 1/2(1) = 4.5.
Therefore, the first vertex is (1, 4.5).

2) When x = 3:
From the second inequality, y can take any value ≤ 0.
From the fourth inequality, y = 5 - 1/2(3) = 3.
Therefore, the second vertex is (3, 3).

3) When y = 0:
From the third inequality, x can take any value between 1 ≤ x ≤ 3.
From the fourth inequality, 1/2x ≤ 5, which implies x ≤ 10.
Therefore, the third vertex is (10, 0).

Now we substitute these vertices into the given function f(x, y) = 2x - y + 2 and find the minimum value:

For (1, 4.5):
f(1, 4.5) = 2(1) - 4.5 + 2 = 0.5

For (3, 3):
f(3, 3) = 2(3) - 3 + 2 = 6

For (10, 0):
f(10, 0) = 2(10) - 0 + 2 = 22

Comparing these values, we see that the minimum value is -0.5, which occurs at the vertex (1, 4.5).

Therefore, the minimum value of f(x, y) = 2x - y + 2 for the given polygonal convex set is -0.5.