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Question

The domain of the function f(x)=sin1(3x2+x1(x1)2)+cos1(x1x+1) is

A
[0,12]
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B
[14,12]{0}
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C
[0,14]
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D
[2,0][14,12]
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Solution

The correct option is B [14,12]{0}
Domain: (3x2+x1(x1)2)[1,1] and x1x+1[1,1]

3x2+x1(x1)214x2x(x1)204x(x14)(x1)20

x(,0][14,1)(1,) (1)

And 3x2+x1(x1)21
2(x+2)(x12)(x1)20

x[2,12] (2)

And x1x+11
2x+10x(1,) (3)

And x1x+11
2xx+10

x(,1)[0,) (4)

Now (1)(2)(3)(4)
x[14,12]{0}

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