Question

Find the domain and range of f(x)=2cotx

Answer 1

Well, first you can rewrite it:
\[f(x) =\frac{2}{tanx}\]

Answer 2

Here, you have two domain restrictions. First, tangent has a restriction (where is it?). Secondly, the denominator (the result of tan(x)) cannot be 0.

Answer 3

i dont think tanx can ever be zero??

Answer 4

tan(x) = sin(x)/cos(x), where is cos(x) = 0?

Answer 5

pi/2?

Answer 6

so would that be the only restriction?

Answer 7

Well, to handle the denominator not being 0, you look for "Where is tangent 0?"

Answer 8

Here, tangent is 0 whenever sin(x) is 0, and sin(x) is 0 at 0 and every pi multiples after that.

Answer 9

So that would be your domain restriction.

Answer 10

yes but doesn't that mean cosx cannot be zero because its on the denominator?

Answer 11

Yes it does, but we've already covered 0.

Answer 12

Killed two birds with one stone in this case.