Question

How do you find the domain and range of `sqrt(8-x)`?

Answer 1

Domain: `[8 , -oo)` , Range: `[0, oo)`

Explanation:

`y= sqrt(8-x)` , Domain : `8-x >= 0 :. 8 >= x or x <= 8 :.` Domain: `[8 , -oo)`

Range : `y >= 0 :.` Range : `[0, oo)` graph{(8-x)^0.5 [-10, 10, -5, 5]} [Ans]

Answer 2

Domain: `x <= 8color(white)("xxx")`or `(-oo,8]`
Range: `[0,+oo)`
`color(white)("XXXXXXXXX")`assuming we are restricted to `RR`, the set of real numbers.

Explanation:

`sqrt(8-x)` is defined (in `RR`) for all values of `x` for which `(8-x) >=0`;
that is for `x <= 8`. [This gives us our "Domain"].

`sqrt("anything")` is defined as the primary root i.e. a value `>=0`
At `x=8`, `color(white)("XXXXXXX")sqrt(8-x)=0`
and as `xrarr-oo`, `color(white)("XX")sqrt(8-x)rarr+oo`
[This gives us our "Range"].