Question

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

Short answer

The domain of the function is $x\in \left(-\infty ,\frac{1}{2}\right]$.

Step-by-step solution

Step 1. By definition of domain of a function.

The given function is $f\left(x\right)=\sqrt{1-2x}$. Now, by definition of domain of function, the domain of the function is defined for all real values of$\left(x\right)$ for which the function is defined.

Step 2. By definition of domain of square root function.

From the square root function $f\left(x\right)=\sqrt{1-2x}$, the domain is defined for all real numbers $\left(x\right)$for which the function $f\left(x\right)=\sqrt{1-2x}$is defined. Since the function $f\left(x\right)=\sqrt{1-2x}$is a square root function, therefore the domain of function is defined for all real numbers for which the expression $1-2x\ge 0$.

role="math" localid="1644585349123" $$\begin{gathered} \text{So,}1-2x\ge 0\text{\hspace{0.33em}gives,} \\ \text{or,}2x\le 1 \\ x\le \frac{1}{2} \end{gathered}$$

Hence the domain of the function is$x\in \left(-\infty ,\frac{1}{2}\right]$

Step 3. Description of steps.

The domain of the function is $x\in \left(-\infty ,\frac{1}{2}\right]$.