Question

How do you find the domain and range of `sqrt{1 - x}`?

Answer 1

Domain : `x <=1 or x in (-oo,1]`
Range : `f(x) >=0 or f(x) in [0,oo)`

Explanation:

`f(x)= sqrt(1-x)` , domain is possible input of `x ; f(x)` is

undefined when `(1-x)<0 :. (1-x)>=0 or 1>=x`

or `x <=1 :.` Domain : `x <=1 or x in (-oo,1]`

Range is resulting output of `f(x) :. f(x) >=0`

Range : `f(x) >=0 or f(x) in [0,oo)`

graph{sqrt (1-x) [-10, 10, -5, 5]}[Ans]