Answer :

We need to find the domain of cos-1 (x2 – 4).

We must understand that, the domain of definition of a function is the set of "input" or argument values for which the function is defined.


We know that, domain of an inverse cosine function, cos-1 x is,


x [-1, 1]


Then,


(x2 – 4) [-1, 1]


Or,


-1 ≤ x2 – 4 ≤ 1


Adding 4 on all sides of the inequality,


-1 + 4 ≤ x2 – 4 + 4 ≤ 1 + 4


3 ≤ x2 ≤ 5


Now, since x has a power of 2, so if we take square roots on all sides of the inequality then the result would be


±√3 ≤ x ≤ ±√5


But this obviously isn’t continuous.


So, we can write as


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