Question

What is the domain and range of `f(x)=sqrt(4-x)`?

Answer 1

Dom `f(x)={x in RR // x>=4}`

Range or Image of `f(x)=[0+oo)`

Explanation:

The expresion under square root must be positive or zero (square roots of negative number are no reals numbers). So

`4-x>=0`

`4>=x`

So the domain is the set of real numbers smaller or equal than 4

In interval form `(-oo,4]` or in set form

Dom `f(x)={x in RR // x>=4}`

Range or Image of `f(x)=[0+oo)`