Find the Domain of the Function
Question:
The domain of the function
\[ f(x)=\frac{x^2+2x+1}{x^2-x-6} \]
is
(a) \(R-\{-2,3\}\)
(b) \(R-\{-3,2\}\)
(c) \(R-\{-2,3]\)
(d) \(R-(-2,3)\)
Solution:
For rational function,
denominator \(\ne0\)
\[ x^2-x-6\ne0 \]
Factorizing,
\[ (x-3)(x+2)\ne0 \]
Therefore,
\[ x\ne3,\,-2 \]
Hence, domain is
\[ \boxed{R-\{-2,3\}} \]
\[ \boxed{\text{Correct Answer: (a)}} \]