Question

How do you find the domain of `y=sqrt(5x+2)`?

Answer 1

`x>=-2/5` or `[-2/5,oo)`

Explanation:

`y=sqrt(5x+2)`, find the domain

In order for y to be defined, the expression under the square root must not be negative. In other words, the expression under the square root must be greater than or equal to zero.

`5x+2>=color(white)a0`
`color(white)(aa)-2color(white)(aa)-2`

`5x>=-2`

`(5x)/5>=-2/5`

`x>=-2/5` is the domain written as an inequality.

`[-2/5,oo)` is the domain written in interval notation