The domain of the function f given by
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(− 3) + 2 (− 3) = 0

i.e  (− 3) (+ 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.

Administrator

Leave a comment

Please enter comment.
Please enter your name.