The domain of the function f given by

Given:

To find: the domain of the given function

Explanation: So the domain of a function consists of all the first elements of all the ordered pairs, i.e., x, so we have to find the values of x to get the required domain

We have

Now for real value

x²-x-6≠0

Splitting the middle term, we get

⇒ x²-3x + 2x-6≠0

⇒ x(x-3) + 2(x-3)≠0

⇒ (x-3)(x + 2)≠0

⇒ x-3≠ 0 or x + 2≠0

⇒ x≠3 or x≠-2

Hence the domain of given function is R-{-2, 3}

So the correct answer is option (A)