Question:
The domain of the function $f$ given by $f(x)=\frac{x^{2}+2 x+1}{x^{2}-x-6}$
(a) R −{−2, 3}
(b) R −{−3, 2}
(c) R −[−2, 3]
(d) R −(−2, 3)
Solution:
$f(x)=\frac{x^{2}+2 x+1}{x^{2}-x-6}$
f(x) is not defined for x2 − x − 6 = 0
i.e x2 − 3x + 2x – 6 = 0
i.e x(x − 3) + 2 (x − 3) = 0
i.e (x − 3) (x + 2) = 0
i.e x = 3 or x = −2
$\therefore$ Domain for $f(x)$ is $R-\{-2,3\}$
Hence the correct answer is option A.
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