# How do you find the domain of f(x)=sqrt(4-x)?

Jul 7, 2016

Df(x) = x in R ; x > 4

#### Explanation:

The domain is the set of $x$-values that can be used to draw the function so,

You are unable to get a square-root of a negative number therefore the value under the square root must be $\ge 0$.

Therefore we need all of the $x$-values that result in the value of $4 - x$ being $\ge 0$.

$4 - x \ge 0$
$4 \ge x$
$x \le 4$

So all $x$-values $\le 4$ will work in the equation. Now we right this in terms of all real numbers:

The Domain of $x$ is all the real numbers expect when $x > 4$ (This produces a negative under the square root)

Df(x) = x in R ; x > 4