Question

Help please

19 points

Answer 1

Domain questions are basically validity checks. Since you cannot have a negative number in a square root without creating an imaginary number, that takes out the bottom two.

A quick tip: substitute the value for x. If the equation is valid (no imaginary numbers, not dividing by 0, etc, that function has the given domain.

ex:

`y = √(x-11) +5\\y = √(-11 -11) + 5\\y = √(-22) + 5`

Negative square roots lead to imaginary numbers so this is not the domain for this problem. The Domain for this one is
`x\geq 11` since that is the lowest possible value of x you can have that is valid.

To answer your question, since I assume you are pressed for time,

`y = √(x + 11) + 5\\y = √(-11 + 11) + 5\\y = √(0) +5\\y = 0 + 5\\y = 5`

so the first one is the function that has the given domain.