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Question : 89 of 150
Marks:
+1,
-0
Solution:
For
f(x) to be defined, we must have
−1≤log2(‌‌x2)≤1⇒2−1≤‌‌x2≤21 [∵ the base
=2>1]
⇒1≤x2≤4......(1)
Now,
1≤x2⇒x2−1≥0‌i.e.‌(x−1)(x+1)≥0
⇒x≤−1‌or‌x≥1.....(2)
Also,
x2≤4⇒x2−4≤0i.e.‌(x−2)(x+2)≤0
⇒−2≤x≤2....(3)
Form (2) and (3), we get the domain of
f={(−∞,−1]∪[1,∞)}∩[−2,2]
=[−2,−1]∪[1,2]
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