Problem preview

A-SSE.1.b Warmup M3-015-A06-V02

Interpret complex polynomial/rational expressions by treating parts as single units.

Build the real domain of a nested radical or rational expression

Problem

Find the real domain of \(1/\sqrt{x~-~3}\). State the condition forced by the square root in the denominator and the resulting interval.

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Because √(x-3) is in the denominator, x-3 must be greater than 0. The real domain is (3,∞).

Only x=3 is excluded, so the real domain is (-∞,3)∪(3,∞).

Because x-3 must be at least 0, the real domain is [3,∞).

The radicand must be negative, so the real domain is (-∞,3).

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Curriculum context

Course: Math III
Standard: A-SSE.1.b
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Interpret complex polynomial/rational expressions by treating parts as single units.
Problem type: Build the real domain of a nested radical or rational expression