Book: RD Sharma - Mathematics (Volume 1)
Chapter: 4. Inverse Trigonometric Functions
Subject: Maths - Class 12th
Q. No. 34 of MCQ
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34
Choose the correct answer
The domain of 
is
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
