Question

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

Answer 1

`x leq 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 `-3x+7.5 geq 0`
Rearranging this a bit we get

`-3x geq -7.5`

`x leq {-7.5}/-3`. (flip the inequality sign since we're dividing by a negative number)

`x leq 2.5`