Final answer:
To evaluate the function f(x,y) = 2x - 3y + xy² at the point (3, -1), substitute x = 3 and y = -1 into the function. Therefore, the value of the function at (3, -1) is 12.
Step-by-step explanation:
Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
To evaluate the function f(x,y) = 2x - 3y + xy² at the point (3, -1), we substitute x = 3 and y = -1 into the function.
Substituting the values, we get:
f(3, -1) = 2(3) - 3(-1) + (3)(-1)² = 6 + 3 + 3 = 12
Therefore, the value of the function at (3, -1) is 12.