The exhaustive domain of the following function is `f(x)=sqrt(x^(12)-x^9+x^4-x+1)` `[0,1]` (b) `[1,oo]` `[-oo,1]` (d) `R`

Options

A. `[0,1]`
B. `[1,oo)`
C. `(-oo,1]`
D. R

Answer

D

Explanation

`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.