Question

What is the domain of the function

Answer 1

`x\geq -6`

Explanation:

The domain of a function is all of the values that
`x` can be under that specific function. In this case, we're asking what values of
`x` allow
`\sqrt{(1)/(3) x+2}` to exist.

In order for square roots to exist, the quantity under the square root must be greater than or equal to
`0`, because you can't take the square root of a negative number. Therefore, we can write the following inequality to solve for
`x`:

`(1)/(3)x+2\geq 0`

Solving this inequality, we get:

`(1)/(3)x+2\geq 0`

`(1)/(3)x\geq -2` (Subtract
`2` from both sides of the inequality to isolate
`x`)

`x\geq -6` (Multiply both sides of the inequality by
`3` to get rid of
`x`'s coefficient)

Hope this helps!