Question

Find the domain of the function. $$g(x)=\sqrt{x^{2}-4}$$

   Find the domain of the function.
$$g(x)=\sqrt{x^{2}-4}$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 64

Instant Answer

Solved by Expert James Kiss

06/01/2020

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The function is defined as the square root of $x^2-4$. Show more…

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Find the domain of the function. $$g(x)=\sqrt{x^{2}-4}$$

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Key Concepts

Solving Quadratic Inequalities

In order to determine the domain of a function that includes a square root of a quadratic expression, one must solve the resulting inequality (set the radicand greater than or equal to zero). Solving such inequalities typically involves factoring or using other algebraic methods to ascertain the intervals where the quadratic expression is non-negative.

Square Root Constraints

When a function involves a square root, the expression inside the square root (known as the radicand) must be non-negative for the function to produce real number outputs. This is because the square root of a negative number is not defined within the real number system.

Domain of a Function

The domain of a function is the set of all input values (typically x-values) for which the function is defined. In problems involving finding domains, one must consider the restrictions imposed by the mathematical expressions in the function, ensuring that operations such as division, square roots, logarithms, etc., are valid.

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