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

The domain of the function `f(x)=sqrt(10-sqrt(x^4-21 x^2))`is`[5,oo)`b

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