1/2 f(-1,1)-2g(-3,3) when f(x,y)= x + 2y-3, g(x,y)=4xy-54/x^2+3y
Just plug in the numbers indicated for x and y and crank out the values of each function. Example: If x= -1 and y=1, corresponding to the (-1,1) point, then
f(x,y) = -1 + (2*1)-3 = -2
(-1/2)f(x,y) = -1
Similarly
g(-3,3) = (4*-3*3)-54/9 + 3*3
= -36 - 6 + 9 = -33
-2 g(-3,3) = 66
Now out it all together
(1/2)f(-1,1)- 2g(-3,3)= ____
To find the value of the expression (1/2)f(-1,1) - 2g(-3,3), we can follow the steps you provided.
First, let's find the value of f(-1,1) by substituting x = -1 and y = 1 into the function f(x,y):
f(-1,1) = (-1) + 2(1) - 3
= -1 + 2 - 3
= -2
Next, we'll find the value of g(-3,3) by substituting x = -3 and y = 3 into the function g(x,y):
g(-3,3) = (4*-3*3) - 54/((-3)^2 + 3(3))
= -36 - 54/((-9) + 9)
= -36 - 54/0
= undefined
It seems that the value of g(-3,3) is undefined because we have division by zero in the denominator. Therefore, we cannot evaluate the full expression (1/2)f(-1,1) - 2g(-3,3) as one of the components is undefined.
In situations like this with undefined values, it's important to carefully check the functions and the provided values to make sure there are no mistakes or unintended issues such as division by zero.
Please double-check the given functions and values to ensure they are accurate and correct, or provide a valid alternative if possible. If you have any further questions, feel free to ask!