• Welcome! The new FreeMathHelp.com forum is live. We've moved from VB4 to Xenforo 2.1 as our underlying software. Hopefully you find the upgrade to be a positive change. Please feel free to reach out as issues arise -- things will be a little different, and minor issues will no doubt crop up.

Adding and Dividing Piecewise Functions and their Domains?

Veru

New member
Joined
Jan 21, 2018
Messages
3
IMG_4971.jpg
We have these two graphs, and these two functions:
A) (F+G)(x)
and
B) (F/G)(x).

And the question is asking what the domains of these two functions are. I am having a lot of trouble understanding how to get to the proper answers. If anybody could explain this question I would be very grateful.

Answers:

A) (-∞, -1]u(1,2]u(3,∞)
and
B) (-∞,-4)u(-4,-1]u(1,2]u(3,∞)
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,701
Some general guidelines:

1) If something isn't in BOTH functions, it cannot be in the SUM.
2) Division offers an additional complication. If your denominator is zero (0), at any point, you'll have to think harder about that point.
 

mmm4444bot

Super Moderator
Staff member
Joined
Oct 6, 2005
Messages
10,143
If I were doing this exercise, I would begin by focusing on the endpoints of the lines shown, in the graphs of piecewise functions F(x) and G(x).

I would label their coordinates. For each of these values of x, I would then calculate F+G.

Next, I would carefully plot the F+G points calculated above, using graph paper. This would give me a visual aid to look at, going forward to consider what's happening at other values of x. And that, in turn, would help me to see where F+G exists (i.e., for which values of x it exists) and where it doesn't. :cool:
 
Top