Questions
if
a
x∈[−1, 0]
b
x∈[0, 1]
c
x∈(−1,1)
d
x∈(1, ∞)
detailed solution
Correct option is C
We have,2x2+4x2+1=2x2+1+2x2+1=2+2x2+1∴ 2<2x2+4x2+1≤4 for all x∈R⇒ π−4<π−2x2+4x2+1<π−2 for all x∈R⇒ −π2<π−2x2+4x2+1<π2 for all x∈R∴ sin−1sin2x2+4x2+1=sin−1sinπ−2x2+4x2+1=π−2x2+4x2+1Hence, sin−1sin2x2+4x2+1<π−3⇒ π−2x2+4x2+1<π−3⇒ 2x2+4x2+1>3⇒ 2+2x2+1⇒2>3>x2+1⇒x2−1<0⇒x∈(−1,1)Talk to our academic expert!
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