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f(x)=sqrt(x^(12)-x^(9)+x^(4)-x+1)...

`f(x)=sqrt(x^(12)-x^(9)+x^(4)-x+1)`

A

`[0,1]`

B

`[1,oo)`

C

`(-oo,1]`

D

R

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=sqrt(x^(12)-x^(9)+x^(4)-x+1)`
We must have `x^(12)-x^(9)+x^(4)-x+1 ge 0 " (1)" `
Obviously, (1) is satisfied by `x in (-oo,0]`.
Aslo, `x^(9)(x^ (3)-1)+x(x^(3)-1)+1 ge 0 AA x in [1,oo).`
Further, `x^(12)-x^(9)+x^(4)-x+1=(1-x)+x^(4)(1-x^(5))+x^(12)` is also satisfied by ` x in (0,1).`
Hence, the domain is R.
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