The function f is defined by \(\mathrm{f(x) = 8x}\). For what value of x does \(\mathrm{f(x) = 72}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{f(x) = 8x}\)
  • We need: the value of x when \(\mathrm{f(x) = 72}\)

• This means we need to solve: \(\mathrm{8x = 72}\)

2. SIMPLIFY to solve for x

• We have the equation: \(\mathrm{8x = 72}\)
• Divide both sides by 8: \(\mathrm{x = 72 ÷ 8 = 9}\)
• Check our work: \(\mathrm{f(9) = 8(9) = 72}\) ✓

Answer: B. 9

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students might confuse what the problem is asking for and think they need to find \(\mathrm{f(8)}\) instead of finding x when \(\mathrm{f(x) = 72}\).

They calculate \(\mathrm{f(8) = 8(8) = 64}\) and think the answer is related to this calculation.

This may lead them to select Choice C (64).

Second Most Common Error:

Conceptual confusion about function notation: Students might think the coefficient 8 in \(\mathrm{f(x) = 8x}\) is somehow the answer they're looking for.

They see \(\mathrm{f(x) = 8x}\) and incorrectly assume \(\mathrm{x = 8}\) without setting up the proper equation.

This may lead them to select Choice A (8).

The Bottom Line:

This problem requires careful reading to understand what value you're solving for (x, not f(x)) and setting up the correct equation based on the given condition.