Q. 345.0( 1 Vote )

# Choose the correc

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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