Domain of definition of Trigonometric Function

Question 5

What is the domain of the function f(x)= ?

1. (3, 5)
2. [2, 3] U [4, 5]
3. [3, 4)
4. (3, 4)

Correct Answer is [3, 4). Choice (3)

Explanatory Answer

Domain of Sin^-1 is from [-1, 1].

So for computing domain of Sin^(x-4), we need to see where (x - 4) lies between -1 and 1.

Or domain of Sin^-1(x - 4) is [3, 5]

Domain of is [-4, 4]

Hence, the domain of is (4,4) as the denominator cannot be zero.

Domain of Cos^-1(3 - x) can be computed similar to how we did domain of Sin^(x-4).

The domain for this component is [2, 4]

The intersection of these three is [3, 4). Choice (3).

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AIEEE Math Problems, Practice Questions and Answers : Listed Topicwise

Sets, Relations & Functions		Permutation Combination		Sequences & Series
Limits, Continuity & Differentiability		Statistics & Probability		Trigonometry
Mathematical Reasoning