Question

Find the domain in `y=sqrt(4-x)`?

Answer 1

`x<=4` or `(-oo,4]`

Explanation:

Since this is a square root, the values inside cannot be lesser that 0. Else, you would end up with an imaginary number. So, with that information, we can write the inequality:

`4-x>=0`

Solve for `x`:

`=> -x>=0-4`

`=>-x>=-4`

Now, when we multiply both sides by a negative, we have to switch the signs:

`(-1)-x<=(-1)-4`

`x<=4`

We can also represent this as:

`(-oo,4]`

And there we have our answer.