The domain of the function `f(x)=sqrt(10-sqrt(x^4-21 x^2))` is `[5,oo)` b. `[-sqrt(21),sqrt(21)]` c. `[-5,-sqrt(21)]uu[sqrt(21),5]uu{0]` d. `(-oo,-5)`

Options

A. `[5,oo]`
B. `[-sqrt(21),sqrt(21)]`
C. `[-5-sqrt(21]]uu[sqrt(21),5)]uu{0}`
D. `(-oo,-5)`

Answer

C

Explanation

We must have `x^(4)-21x^(2) ge 0 and 10-sqrt(x^(4)-21x^(2))ge0`
`rArr" "x^(2)(x^(2)-21)ge0" (1)"`
`"and "100gex^(4)-21x^(2)" (2)"`
Eq. (1) gives x = 0 or `x le-sqrt(21)or x ge sqrt(21)`
`"Eq. (2)" rArrx^(4)-21x^(2)-100le0`
`rArr" "(x^(2)-25)(x^(2)+4)le0`
`rArr" "x^(2)-25le0" "("as "x^(2)+4 gt0" always")`
`rArr" "-5lexle5`
Domain is given by `[-5,-sqrt(21)]cup[sqrt(21),5]` and x=0.`