Question

$g(x)=\sqrt{x+2}, x \geq-2$

Name: Problem 61, Chapter 9: Intermediate Algebra for College Students
Uploaded: 2021-08-04T22:34:44-08:00
Duration: 1 min 12 s
Channel: Carson Merrill
Description: g(x)=√(x+2), x ≥-2

   $g(x)=\sqrt{x+2}, x \geq-2$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 9, Problem 61

Instant Answer

Solved by Expert Carson Merrill

08/04/2021

Step 1

Since the function has a square root, we know that the value inside the square root must be greater than or equal to 0. So, we have: x + 2 ≥ 0 Solving for x, we get: x ≥ -2 This means that the domain of the function is all real numbers greater than or equal to Show more…

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$g(x)=\sqrt{x+2}, x \geq-2$

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Key Concepts

Radical Functions

A radical function involves a variable under a radical symbol, typically a square root when dealing with real functions. In such functions, the expression inside the radical (the radicand) must satisfy certain conditions (usually non-negativity for even-indexed roots) to ensure the function produces real outputs.

Domain of a Function

The domain of a function is the set of all possible input values for which the function is defined. For a square root function, the radicand must be greater than or equal to zero, which directly determines the domain of the function.

Function Transformations

Function transformations involve modifications to a basic function, such as shifts, stretches, or reflections, that change its graph. In the given function, the input is modified by adding a constant, which results in a horizontal shift of the basic square root graph.

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