How do you find the domain & range for #(1/2)tan(x)#?

1 Answer
KillerBunny
Oct 16, 2015

Domain: #\mathbb{R} \setminus {pi/2+kpi,\ k \in \mathbb{Z} } #

Range: #(-infty, infty)#.

Explanation:

The range is the same of the tangent, because if it is legit to compute #tan(x)#, then dividing that value by #2# is surely ok.

So, the domain is the real set minus the points in which #cos(x)=0#, i.e.

#\mathbb{R} \setminus {pi/2+kpi,\ k \in \mathbb{Z} } #

The same goes for the range: since the tangent ranges from #-infty# to #infty#, half of this range is still #(-infty, infty)#.

Note that this is true only because the interval is infinite in both direction, if the original range of #f(x)# is #[a,b]#, then the range of #f(x)/2# is #[a/2, b/2]#.

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