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Question

The domain of the function fx=cos-1log3x4 is


A

4,12

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B

0,3

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C

43,4

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D

43,12

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Solution

The correct option is D

43,12


Explanation for the correct options:

Finding the domain of the function fx:

We know that cos-1x exists if -1x1

therefore, we can define the above function as:

-1log3x41

We know that

logax=bx=ab

Since,

log3x4-1x43-1

Then, we can rewrite the inequality as:

x431x31×4x12

And

x43-1x413x43

Hence, the domain of the function fx is 43,12.

Therefore the correct answer is option D.


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