Q. 8.142 - Intermediate Algebra

Question

Find the domain of the function, $f\left(x\right)=\sqrt{4-5x}$, Write the domain in interval notation.

Step-by-Step Solution

Answer

The domain of $f\left(x\right)=\sqrt{4-5x}$ is all values $x\le \frac{4}{5}$ and in interval notation $(-\infty ,\frac{4}{5}]$

Step 1. Given Information

The function $f\left(x\right)=\sqrt{4-5x}$

Since the function,$f\left(x\right)=\sqrt{4-5x}$, has a radical with an index of 2, which is even, we know the radicand must be greater than or equal to 0.

Step 2. Finding the domain

We set the radicand to be greater than or equal to 0 and then solve to find the domain.$$\begin{gathered} 4-5x\ge 0 \\ 4\ge 5x \\ \frac{4}{5}\ge x \\ x\le \frac{4}{5} \end{gathered}$$

interval notation is