\(\mathrm{g(x) = 3(8 - x)}\) For the function g defined above, what is the value of \(\mathrm{g(2)}\)?...

1. TRANSLATE the problem requirement

• Given: \(\mathrm{g(x) = 3(8 - x)}\)
• Find: \(\mathrm{g(2)}\)
• What this means: Substitute \(\mathrm{x = 2}\) into the function

2. SIMPLIFY through substitution and calculation

• Substitute \(\mathrm{x = 2}\): \(\mathrm{g(2) = 3(8 - 2)}\)
• Work inside parentheses first: \(\mathrm{g(2) = 3(6)}\)
• Multiply: \(\mathrm{g(2) = 18}\)

Answer: D (18)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution - Order of operations confusion: Students might incorrectly calculate \(\mathrm{3 \times 8 - 2 = 24 - 2 = 22}\), forgetting that the subtraction should happen inside the parentheses first.

This may lead them to select Choice B (22).

Second Most Common Error:

Incomplete SIMPLIFY process: Students correctly find \(\mathrm{8 - 2 = 6}\) but forget to multiply by 3, stopping at just the result inside the parentheses.

This may lead them to select Choice A (6).

The Bottom Line:

This problem tests whether students understand function notation and can systematically follow order of operations. The key is remembering that parentheses must be evaluated before multiplication, and that finding \(\mathrm{g(2)}\) requires complete substitution and simplification.