The correct answer is option (B):
35
Let's break this problem down step by step. We're given two functions, f(a, b) and g(a, b), and we need to evaluate them at specific points and then subtract the results.
First, let's find f(6, 3). The function is defined as f(a, b) = a^2 + b^2. So, substituting a = 6 and b = 3, we get:
f(6, 3) = 6^2 + 3^2 = 36 + 9 = 45.
Next, let's find g(8, 4). The function is defined as g(a, b) = (2 / b^2) * (a^2 + b^2). Substituting a = 8 and b = 4, we get:
g(8, 4) = (2 / 4^2) * (8^2 + 4^2) = (2 / 16) * (64 + 16) = (1/8) * 80 = 10.
Finally, we need to find f(6, 3) - g(8, 4). We found that f(6, 3) = 45 and g(8, 4) = 10, so:
f(6, 3) - g(8, 4) = 45 - 10 = 35.
Therefore, the correct answer is 35.