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Question

Find the domain of the functionf(x)=[2(x2-x+1)-1(x+1)-2x-1(x3+1)]


A

(-,2]-{-1}

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B

(-,2)

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C

]-1,2]

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D

None of these

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Solution

The correct option is A

(-,2]-{-1}


Explanation for correct option:

Step 1: Set the terms inside the root symbol to be greater than or equal to 0.

We have givenf(x)=[2(x2-x+1)-1(x+1)-2x-1(x3+1)].

2(x2-x+1)-1(x+1)-2x-1(x3+1)02(x2-x+1)-1(x+1)-2x-1(x+1)(x2-x+1)02(x+1)-(x2-x+1)-(2x-1)(x+1)(x2-x+1)02x+2-x2+x-1-2x+1(x+1)(x2-x+1)0-x2+x+2(x+1)(x2-x+1)0-(x+1)(x-2)(x+1)(x2-x+1)0

From abovex-1….(1).

Step 2: Find the points where the function changes the signs.

-(x-2)(x2-x+1)0{(x2-x+1)>0a>0&D<0}-(x-2)0(x-2)0x2.......(2)

So,

x(-,2]-{-1}

Hence, option(A) is the correct option.


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