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Question

The domain of cos1x32log10(4x) is

A
(1,4)
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B
[1,4)
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C
(1,4]
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D
[1,4]
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Solution

The correct option is D [1,4)

The domain of cos1x32log10(4x) is

let cos1x32=θcosθ=x32


1cosθ1

1x321

1x321


2x32

2+3x2+3

1x5


So, 1x5(1)

log10(4x)

as log is only defined for positive numbers

4x>0

4>x(2)
Taking intersection on both (1) and (2)
We get
1x<4 or x[1,4)


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