Question

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

Answer 1

`D_f = {x <= 8 }` and

`R_f = { 0<=y<∞}` where `y = (8-x)^(1/2)`

Explanation:

Since the given function is a square root function so the only NON-NEGATIVE values are allowed in the Domain and the Range will also be having NON-NEGATIVE Real numbers only.

For Domain, `D_f` :

`8-x>=0`
`rArrx-8<=0`
`rArrx <= 8`

and we can see that this function will acquire every positive value and Zero also (when `x=8`).

Thus the Range of function, `R_f = { 0<=y<∞}`