The domain of the function f defined by is equal to

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

4-x≥0 and x²-1>0

⇒ 4≥x and x²>1

⇒ x≤4 and -1>x>1

⇒ x≤4 and x>1 and x<-1

⇒ x∈ (-∞, -1)∪(1, 4]

Hence the domain of given function is (-∞, -1)∪(1, 4]

So, the correct answer is option (A)