Question

what is the domain of the function ( y = ln(x + 2) )?
( x < -2 )
( x > -2 )
( x < 2 )
( x > 2 )

Explanation:

Step1: Determine the domain condition

For the function \(y = \ln(u)\), the argument \(u\) must satisfy \(u>0\). Here \(u=x + 2\).

Step2: Solve the inequality

Set up the inequality \(x+2>0\). Subtract 2 from both sides: \(x+2-2>0 - 2\), which simplifies to \(x>-2\).

Answer:

\(x > - 2\) (the second option)