Question

Find the domain of the function. $$f(x)=\sqrt{1-2 x}$$

   Find the domain of the function.
$$f(x)=\sqrt{1-2 x}$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 63

Instant Answer

Solved by Expert James Kiss

06/01/2020

Step 1

In other words, we need to find the values of $x$ that satisfy the inequality $1-2x \geq 0$. To solve this inequality, we can isolate $x$ by subtracting $1$ from both sides and then dividing by $-2$. Show more…

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Find the domain of the function. $$f(x)=\sqrt{1-2 x}$$

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Key Concepts

Radicand

The radicand is the expression contained within the square root. For functions involving square roots, ensuring that the radicand is non-negative is essential to maintain a real number output, thereby affecting the function's domain.

Domain of a Function

The domain of a function is the set of all input values for which the function is defined. This concept is crucial because it determines which values can be fed into the function to produce a valid output, taking into account any restrictions like divisions by zero or non-real operations.

Square Root Function

Square root functions require that the expression under the square root, known as the radicand, is non-negative because the square root of a negative number is not defined within the real numbers. This necessity directly influences the domain of such functions.

Inequalities

Solving inequalities is often required when determining the domain of a function, especially for functions involving square roots. One sets up an inequality (e.g., the radicand must be at least zero) and solves it to find the range of permissible input values.

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