Question

If \( f(a,b) = a^2+b^2 \) and \( g(a,b) = \frac{2}{b^2}\left[a^2+b^2\right] \), then what is the value of \( f(6, 3) - g(8, 4) \)?

• A. 30
• B. 35
• C. 40
• D. 45

Hint:

Substitute the given values directly into each function definition, simplify, then subtract.

Answer 1

The Correct Option is B

Step 1: Evaluate f(6, 3).
\( f(a,b) = a^2+b^2 \), so \( f(6,3) = 6^2+3^2 = 36+9 = 45 \).

Step 2: Evaluate g(8, 4).
\( g(a,b) = \frac{2}{b^2}\left[a^2+b^2\right] \), so \( g(8,4) = \frac{2}{4^2}\left[8^2+4^2\right] = \frac{2}{16}(64+16) = \frac{2}{16}(80) \).
This simplifies to \( g(8,4) = \frac{160}{16} = 10 \).

Step 3: Subtract to get the value.
\( f(6,3) - g(8,4) = 45 - 10 = 35 \).
The other choices are traps: 45 is f(6,3) alone, 40 comes from misreading the factor as 1, and 30 from a sign slip.

Final Answer:
The value is 35, which is option (b). \[ \boxed{35} \]