The function g is defined by \(\mathrm{g(x) = 18 - \sqrt{x}}\). What is the value of \(\mathrm{g(64)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{g(x) = 18 - \sqrt{x}}\)
  • Need to find: \(\mathrm{g(64)}\)

• This tells us we need to substitute \(\mathrm{x = 64}\) into the function

2. SIMPLIFY by substitution and evaluation

• Substitute \(\mathrm{x = 64}\): \(\mathrm{g(64) = 18 - \sqrt{64}}\)

• Evaluate the square root: \(\mathrm{\sqrt{64} = 8}\) (since \(\mathrm{8 \times 8 = 64}\))

• Complete the calculation: \(\mathrm{g(64) = 18 - 8 = 10}\)

Answer: B. 10

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Incorrectly calculating \(\mathrm{\sqrt{64}}\)

Students might confuse \(\mathrm{\sqrt{64}}\) with other operations, such as thinking \(\mathrm{\sqrt{64} = 16}\) (perhaps confusing it with \(\mathrm{64 \div 4}\)). If they calculate \(\mathrm{\sqrt{64} = 16}\), then \(\mathrm{g(64) = 18 - 16 = 2}\).

This leads them to select Choice A (2).

Second Most Common Error:

Poor SIMPLIFY execution: Sign error in final calculation

Students correctly find \(\mathrm{\sqrt{64} = 8}\) but then add instead of subtract: \(\mathrm{g(64) = 18 + 8 = 26}\).

This leads them to select Choice D (26).

Third Most Common Error:

Weak TRANSLATE reasoning: Misunderstanding the function structure

Students might ignore the square root entirely and just evaluate \(\mathrm{g(64) = 18}\), thinking the \(\mathrm{\sqrt{x}}\) part doesn't apply or missing it completely.

This leads them to select Choice C (18).

The Bottom Line:

This problem tests basic function evaluation skills, but students often struggle with either calculating square roots of perfect squares or making simple arithmetic errors under test pressure. The key is careful step-by-step execution.