The function g is defined by \(\mathrm{g(x) = \frac{640}{x} + 8}\). What is the value of \(\mathrm{g(x)}\) when x =...

1. TRANSLATE the problem information

• Given: Function \(\mathrm{g(x) = \frac{640}{x} + 8}\)
• Find: The value of \(\mathrm{g(x)}\) when \(\mathrm{x = 8}\)
• What this means: Substitute \(\mathrm{x = 8}\) into the function to find \(\mathrm{g(8)}\)

2. SIMPLIFY by substitution and calculation

• Substitute \(\mathrm{x = 8}\): \(\mathrm{g(8) = \frac{640}{8} + 8}\)
• Calculate the division first (order of operations): \(\mathrm{640 \div 8 = 80}\)
• Add 8 to complete the calculation: \(\mathrm{80 + 8 = 88}\)

Answer: C (88)

Why Students Usually Falter on This Problem

Most Common Error Path:

Incomplete SIMPLIFY execution: Students correctly substitute and calculate \(\mathrm{\frac{640}{8} = 80}\), but then forget to add the remaining 8.

They see \(\mathrm{\frac{640}{8} = 80}\) and immediately think they're done, overlooking that the original function has "\(\mathrm{+ 8}\)" at the end. This incomplete calculation makes them confident in selecting Choice B (80).

The Bottom Line:

This problem tests careful attention to all parts of a function. The arithmetic is straightforward, but students must complete every step of the calculation, not just the division portion.