Final answer:
To find y(2) at (3,1), substitute x = 3 and y = 1 into the given equation. By solving for f(3), we can determine that y(2) = f(3) = 271.
Step-by-step explanation:
To find y(2) at (3,1), we need to substitute x = 3 and y = 1 into the given equation:
y³ + [f(x)]³ = 6xy + 326
(1)³ + [f(3)]³ = 6(3)(1) + 326
1 + [f(3)]³ = 18 + 326
[f(3)]³ = 345
Since we know that f(4) = 74, we can write [f(3)] as follows:
[f(3)] = [f(4) - (f(4) - f(3))]
Plugging in the values, we get:
[f(3)] = 74 - (74 - f(3))
345 = 74 - (74 - f(3))
f(3) = 345 - 74
f(3) = 271
Therefore, y(2) = f(3) = 271.