# The domain of the function f defined by is equal toA. (– ∞, – 1) ∪ (1, 4]B. (– ∞, – 1] ∪ (1, 4]C. (– ∞, – 1) ∪ [1, 4]D. (– ∞, – 1) ∪ [1, 4)

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)

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