Question

Find the domain of the function. $$g(x)=\sqrt{7-3 x}$$

   Find the domain of the function.
$$g(x)=\sqrt{7-3 x}$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 62

Instant Answer

Solved by Expert James Kiss

06/01/2020

Step 1

The square root function is defined for non-negative values. Therefore, the expression inside the square root must be greater than or equal to zero. For the function \( g(x) = \sqrt{7 - 3x} \), we need \( 7 - 3x \geq 0 \). Show more…

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Find the domain of the function. $$g(x)=\sqrt{7-3 x}$$

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Key Concepts

Domain of a Function

The domain is the set of all input values for which the function is defined. Determining the domain involves identifying restrictions from operations like division or taking square roots, ensuring that there is no violation of mathematical rules.

Square Root Function

A square root function involves computing the square root of an expression. In the realm of real numbers, the value inside the square root (the radicand) must be nonnegative, as the square root of a negative number is not defined.

Inequality Constraints for Radicals

When a function contains a square root, setting the radicand greater than or equal to zero yields an inequality that must be solved to identify all acceptable input values, thus determining the function's domain.

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