# How do you find the domain of g(x)=4sqrt(-3x+7.5)?

Apr 5, 2018

$x \le q 2.5$

#### Explanation:

The domain is the set of values that x can have for the function to be defined.

That being said, the number inside the radical must be greater than or equal to zero, otherwise we'll get a complex number, which I'm assuming you might not want.

This gives us the equation $- 3 x + 7.5 \ge q 0$
Rearranging this a bit we get

$- 3 x \ge q - 7.5$

$x \le q \frac{- 7.5}{-} 3$. (flip the inequality sign since we're dividing by a negative number)

$x \le q 2.5$