Problem preview

A-SSE.1.b Warmup M3-015-A06-V03

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 \(\sqrt{x^2~+~4}/x\). Analyze the radicand and the outside denominator separately, then state the resulting intervals.

Answer choices

Choose your path.

Preview only

Treating the entire quotient as the radicand gives the real domain (0,∞).

Factoring x²+4 gives critical values -2 and 2, so the real domain is (-∞,-2]∪[2,∞).

The radicand x²+4 is positive for every real x, but x cannot be 0. The real domain is (-∞,0)∪(0,∞).

The radicand is nonnegative for every real x, so every real x is in the domain.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Inside Gozunta

More than a preview

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now

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