# If g(x) = 5 - sqrt(x+30), how do you solve g(-34)?

Oct 15, 2015

$g \left(- 34\right) = 5 - 2 i$

#### Explanation:

If $g \left(\textcolor{red}{x}\right) = 5 - \sqrt{\textcolor{red}{x} + 30}$
then
$g \left(\textcolor{red}{- 34}\right) = 5 = \sqrt{\textcolor{red}{- 34} + 30}$

$\textcolor{w h i t e}{\text{XXX}} = 5 - \sqrt{- 4}$

$\textcolor{w h i t e}{\text{XXX}} = 5 - 2 i$ where $i = \sqrt{- 1}$

Oct 15, 2015

Unvalid expression in real number set, $- 5 - 2 i$ in the complex one.

#### Explanation:

There's nothing to "solve" actually, you simply need to evaluate the function in the point. This means to substitute every "$x$" appearing in the formula with the number $- 34$.

Doing so we get

$5 - \sqrt{- 34 + 30} = 5 - \sqrt{- 4}$.

Now, if you're working with real numbers, you can't calculate the square root of a negative number. This means that $- 34$ was not part of the domain of the function, i.e. it was an illegitimate value to give as an input.

If you're working with complex number, then $\sqrt{- 4} = 2 i$, and so the result is $- 5 - 2 i$.