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Question

The domain of the function fx=cosxis


A

3π2,2π

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B

0,π2

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C

-π2,π2

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D

0,π23π2,2π

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Solution

The correct option is C

-π2,π2


Finding the domain of the function fx:

We have the given function as: fx=cosx

Define the above function as:

cosx0, since if the value if less than zero, it will become an imaginary function.

0cosx1, Since the value of cosx lies between [0,1].

cosx lies between 0to1. Then, x lies between 1st or 4th quadrant

0xπ2or3π2x2πx0,π23π2,2π

We can rewrite it as:

x-π2,π2

Hence, the domain of the given function is -π2,π2

Therefore, the correct answer is option (C).


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