Question

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

Answer 1

`g(-34) = 5-2i`

Explanation:

If `g(color(red)(x))=5-sqrt(color(red)(x)+30)`
then
`g(color(red)(-34)) = 5=sqrt(color(red)(-34)+30)`

`color(white)("XXX")=5-sqrt(-4)`

`color(white)("XXX")=5-2i` where `i=sqrt(-1)`

Answer 2

Unvalid expression in real number set, `-5-2i` 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)=2i`, and so the result is `-5-2i`.