Questions: Find the domain of the function (f(x)=sqrt5x-2) In interval form, the domain of (f) is (square)

Transcript text: Find the domain of the function $f(x)=\sqrt{5 x-2}$ In interval form, the domain of $f$ is $\square$

Solution

Solution Steps

To find the domain of the function $ f(x) = \sqrt{5x - 2} $, we need to determine the values of $ x $ for which the expression under the square root is non-negative. This means solving the inequality $ 5x - 2 \geq 0 $.

Step 1: Understand the Problem

We need to find the domain of the function $ f(x) = \sqrt{5x - 2} $. The domain of a function is the set of all possible input values (x-values) that make the function defined.

Step 2: Identify the Condition for the Square Root Function

For the square root function $ \sqrt{5x - 2} $ to be defined, the expression inside the square root must be non-negative. Therefore, we need: \[ 5x - 2 \geq 0 \]

Step 3: Solve the Inequality

Solve the inequality $ 5x - 2 \geq 0 $: \[ 5x - 2 \geq 0 \] Add 2 to both sides: \[ 5x \geq 2 \] Divide both sides by 5: \[ x \geq \frac{2}{5} \]

Step 4: Express the Domain in Interval Form

The domain of $ f(x) $ is all $ x $ such that $ x \geq \frac{2}{5} $. In interval notation, this is: \[ \left[ \frac{2}{5}, \infty \right) \]