Question

Find the domain of the function. $$y=\sqrt{3 x-10}$$

Short answer

The domain of the function \(y = \sqrt{3x - 10}\) is \([10/3, +\infty)\).

Step-by-step solution

Set the Radicand Greater Than or Equal to Zero

To find the domain of the function, we can start by setting the radicand, \(3x - 10\), greater than or equal to zero: \(3x - 10 >= 0\). This is because the square root of a negative number is not real, hence for a real domain, \(3x - 10\) must be zero or positive.

Solve the Inequality for x

Next, we need to solve the inequality \(3x - 10 >=0\) for x. We can do this by adding 10 to both sides of the inequality to isolate \(3x\): \(3x >= 10\). Then, we divide both sides by 3, getting: \(x >= 10/3\).

Write the Final Answer

From the solved inequality, we have our answer. The domain of the function is all real numbers x that are greater than or equal to \(10/3\). Thus the domain is \([10/3, +\infty)\).