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Question
The domain of the function f(x)=√10−√x4−21x2 is
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Solution
The correct option is C
We must have x4−21x2≥0 and 10−√x4−21x2≥ 0⇒ x2(x2−21)≥0−−−−(1)and 100 ≥ x4−21x2−−−−−(2)(1) gives x=0 or x≤−√21 or x≥√21(2) ⇒ x4−21x2−100≤0⇒ (x2−25)(x2+4)≤0⇒ x2−25≤0 (as x2+4>0 always)⇒ −5≤x≤5Domain is given by [−5,−√21]∪[√21,5] and x=0.
We must have x4−21x2≥0 and 10−√x4−21x2≥ 0⇒ x2(x2−21)≥0−−−−(1)and 100 ≥ x4−21x2−−−−−(2)(1) gives x=0 or x≤−√21 or x≥√21(2) ⇒ x4−21x2−100≤0⇒ (x2−25)(x2+4)≤0⇒ x2−25≤0 (as x2+4>0 always)⇒ −5≤x≤5Domain is given by [−5,−√21]∪[√21,5] and x=0.
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