Question

The domain of the function f given by $f\left(x\right)=\frac{x^2+2x+1}{x^2-x-6}$
(a) R −{−2, 3}
(b) R −{−3, 2}
(c) R −[−2, 3]
(d) R −(−2, 3)

Answer 1

f(x) = $\frac{x^2+2x+1}{x^2-x-6}$
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.