Correct Answer - Option 2 : {x ∶ x ∈ R and x > -2 and x ≠ -1}
\(P\left( x \right) = \frac{x}{{\log \left( {2 + x} \right)}}\)
P(x) is defined, if log (2 + x) is real and also log (2 + x) ≠ 0.
Now,
1) log (2 + x) will be real if
2 + x > 0
x > -2
2) log (2 + x) ≠ 0 is satisfied if
2 + x ≠ 1
x ≠ -1
∴ The required domain of definition of P(x) is:
{x ∶ x ϵ R and x > -2 and x ≠ -1}