Question

In the set of real numbers, what is the domain of `f(x)=sqrt(x+5)`?

Answer 1

The domain, or allowed values of `x`, is `x>=-5`. In interval notation, the domain is `[-5,oo)`.

Explanation:

For real numbers, the expression under the square root must be greater than or equal to zero. In other words, you can't take a square root of a negative.

`f(x)=sqrt(x+5)`

`x+5 >= color(white)a0`
`color(white)(a)-5color(white)(a^2)-5color(white)(aaa)`Subtract `5` from both sides

`color(white)(aa)x>= -5`

In interval notation, `x>= -5` is written `[-5, oo)`