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Question

For the function f(x)=sin2x, xR, which of the following is/are correct ?

A
For x<0, f(x)<sin1
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B
x=0 is an asymptote
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C
y=0 is an asymptote
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D
For f(x)=0, x=log2(nπ),nZ
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Solution

The correct options are
A For x<0, f(x)<sin1
C y=0 is an asymptote
f(x)=sin2x

f(x)=0sin2x=02x=nπ, nNx=log2(nπ), nN

When
x, sin2x0
So, y=0 is an asymptote.

For x<0,
0<2x<1
f(x)=sin2xf(x)=cos2x×2xln20
So f(x) is a increasing function.
f(x)<f(0)f(x)<sin1

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