Problem preview

F-IF.8 Warmup M3-027-A14-V03

Rewrite functions in equivalent forms to reveal and explain useful properties.

Decide whether a proposed rewrite keeps the same function and the same restrictions

Problem

Does this rewrite preserve the original restrictions: \(\ln(x^2)\) rewritten as \(2\ln(x)\)?

Answer choices

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Yes; the power rule says ln(x²) equals 2ln(x), so the rewrite keeps exactly the same restrictions.

No; the rewrite is not valid because ln(x²) already requires x > 0, so both expressions have the same positive-only domain.

No; ln(x²) is defined for every real x except 0, but 2ln(x) works only when x > 0, so the rewrite loses the negative x-values.

Yes; since x² is positive for both positive and negative x, 2ln(x) must also include negative x in its domain.

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Curriculum context

Course: Math III
Standard: F-IF.8
Category: Functions
Domain: Interpreting Functions
Objective: Rewrite functions in equivalent forms to reveal and explain useful properties.
Problem type: Decide whether a proposed rewrite keeps the same function and the same restrictions