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

Mar 19, 2018

$x \le 4$ or $\left(- \infty , 4\right]$

#### 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:

$4 - x \ge 0$

Solve for $x$:

$\implies - x \ge 0 - 4$

$\implies - x \ge - 4$

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

$\left(- 1\right) - x \le \left(- 1\right) - 4$

$x \le 4$

We can also represent this as:

$\left(- \infty , 4\right]$

And there we have our answer.