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 find the values of x that are not in the domain of the function f(x) = (2 - x^2) / (x + 5), we need to identify the values of x that would make the denominator equal to zero.
In this case, the function is not defined for x = -5 because when x = -5, the denominator (x + 5) becomes zero. Division by zero is undefined in mathematics, so -5 is not in the domain of the function f(x).
To find the minimum value of the function f(x, y) = 2x - y + 2 within the polygonal convex set determined by the system of inequalities:
x ≥ 1
x ≤ 3
y ≤ 0
(1/2)x + y ≤ 5
We can proceed with the following steps:
1. Graph the inequalities on a coordinate plane to determine the feasible region.
- Plot the lines for each inequality and shade the region that satisfies all the conditions.
2. Find the vertices of the feasible region.
- The vertices of the feasible region are the points where the lines intersect.
- In this case, the vertices will be the points where the lines x = 1, x = 3, y = 0, and (1/2)x + y = 5 intersect.
3. Plug in the coordinates of the vertices into the function f(x, y) = 2x - y + 2.
- Evaluate the function at each vertex using the given coordinates.
- The minimum value of f(x, y) will be the smallest output among all the vertices.
By following these steps, you can find that the minimum value of f(x, y) is -0.5 within the given constraints and feasible region.