# How do you find the domain of  f(x) = 1/(sqrt(5 - x) - 1)?

May 18, 2017

The domain, in this case. is all real numbers except for the values of $x$ that would result in a non-real value.

#### Explanation:

If $x$ causes the denominator to be $0$, then the function would be undefined at that point.

$0 = \sqrt{5 - x} - 1$

$1 = \sqrt{5 - x}$

${1}^{2} = 5 - x$

$1 = 5 - x$

$- 4 = - x$

$x = 4$

The function would also be imaginary at $x$ if there was a square root of a negative value. Therefore...

$\sqrt{5 - x} \ge 0$

$5 - x \ge {0}^{2}$

$5 \ge x$

The domain of $x$ is all real values less than or equal to $5$ and not including $4$.