Problem preview
F-BF.1.b Warmup M3-018-A10-V01

Combine studied function types arithmetically to build models.

Determine the domain of a combined function by combining all input restrictions

Problem

Determine the domain of this combined function: \(\sqrt{x-2}+\ln(x+1)\)

Big Picture

What this problem is really about

A combined expression is defined only where every component is defined, so find each restriction separately and intersect them. Square roots allow a zero radicand, while logarithms require a strictly positive argument; those different boundary rules decide whether an endpoint survives. Checking the limiting endpoint in both components is the cleanest final safeguard.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
F-BF.1.b
Category
Functions
Domain
Building Functions
Objective
Combine studied function types arithmetically to build models.
Problem type
Determine the domain of a combined function by combining all input restrictions