Question

How do you find the domain and range of `sqrt(x+5)`?

Answer 1

Domain`: {x in RR | x geq - 5}`

Range`: {f(x) in RR | f(x) geq 0}`

Explanation:

We have: `f(x) = sqrt(x + 5)`

The domain of any square root function is dependent on its argument.

The argument must be greater than or equal to zero:

`Rightarrow x + 5 geq 0`

`Rightarrow x geq - 5`

The square root function never produces a negative result.

So the range will be greater than or equal to zero as well:

`Rightarrow f(x) geq 0`

Therefore, for the function `f(x) = sqrt(x + 5)`, the domain is `{x in RR | x geq - 5}` and the range is `{f(x) in RR | f(x) geq 0}`.