Final Answer:
The value of g(2, -1) is cos(2 - 2) = cos(0) = 1.
Step-by-step explanation:
To evaluate g(2, -1), substitute the given values into the function g(x, y) = cos(x + 2y). In this case, x = 2 and y = -1. Plugging these values in, we get g(2, -1) = cos(2 + 2 × (-1)). Simplifying the expression inside the cosine function gives cos(2 - 2), which is cos(0). The cosine of 0 radians is 1, so the final result is g(2, -1) = 1.
The function g(x, y) = cos(x + 2y) involves the cosine of the sum of x and 2y. In this context, g(2, -1) evaluates to the cosine of 2 - 2 × 1, which simplifies to cos(0). The cosine function produces a maximum value of 1 when the input is 0 radians. Therefore, g(2, -1) equals 1.
In conclusion, the evaluation of g(2, -1) results in the value 1. This is obtained by substituting the given values into the function and simplifying the expression within the cosine function. The final answer reflects the mathematical outcome of the specified function for the given input values.