Help With Composite Function: h(x) = -x (-1<=x<0), x (0<=x<=1), g(x) = -tan(x)

[matheyyy]

Hi all,
I have this composite function that I am trying to solve which involves a domain restriction of g(x). The real trouble I have here is trying to articulate what the domain of g(x) is, since it's an interval on a tan graph repeated an infinite amount of times. I had a go at it (see attached) but I am unsure whether or not it's correct. Thanks in advance guys!

 

[blamocur]

What does [imath]\left[\frac{\pi}{4}\pm n\pi, n\pi\right][/imath] mean? Is this is an interval, then what are the endpoints?

Also, what does [imath]x\cup...[/imath] mean in the definition of [imath]h(g(x))[/imath] ?

 

[Dr.Peterson]

Hi all,
I have this composite function that I am trying to solve which involves a domain restriction of g(x). The real trouble I have here is trying to articulate what the domain of g(x) is, since it's an interval on a tan graph repeated an infinite amount of times. I had a go at it (see attached) but I am unsure whether or not it's correct. Thanks in advance guys!View attachment 35250

I think you probably meant

​

But you show the identical domain for both pieces of the function, so clearly something is wrong.

I think a good thing to do to correct this would be to start with one specific value of n (that is, one of the intervals involved), write out what that interval is, and correcting it as needed.

What I myself might have done first is to observe that h(x) = |x|, restricted to the interval [-1, 1].

 

[Steven G]

You are given what g(x) is but I don't understand the restriction you imposed on g(x).

For the record tan(0) = 0, not undefined. tan(x) goes from -infinity to +infinity.