[tex]\text{Consider the function}\\
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y=6\tan(x/2)-3\\
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\text{to find the x-intercepts of the graph of the function, we put y=0.}\\
\text{so we get}\\
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6\tan(x/2)-3=0\\
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\Rightarrow 6\tan(x/2)=3\\
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\Rightarrow \tan(x/2)=\frac{3}{6}\\
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\Rightarrow \tan(x/2)=\frac{1}{2}\\
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\Rightarrow \frac{x}{2}=\tan^{-1}\left (\frac{1}{2} \right )[/tex]
[tex]\Rightarrow \frac{x}{2}\approx 0.4636\\
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\text{the period of tangent is }\pi, \text{ so we have}\\
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\Rightarrow \frac{x}{2}\approx 0.4636+n\pi\\
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\Rightarrow x=2( 0.4636+n\pi)\\ \\
\Rightarrow x=0.9273+2n\pi\\
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\text{Hence the x-itnercepts of the function are: }(0.9273+2n\pi,\ 0)[/tex]
