Expert: Abe Mantell - 9/5/2005

Question
I'm gonna go out on a limb here and ask 3 questions/problems. Even if you only answer 1 that would be great!

1. My book says this, "Find (a) (f + g)(x), (b) (f - g)(x), (c) (fg)(x), and (d) (f/g)(x). What is the domain of f/g?"

f(x) = x/ x + 1 (that's x over x + 1), g(x) = x^3

From there I'm pretty much confused.

2. "Use a graphing utility to graph the functions f, g, and f + g in the same viewing window." (I have a TI83.)

f(x) = (1/2)x (I added the parentheses in so you'd know it was 1/2), g(x) = x - 1

If I knew what I was suppose to do, maybe I could graph it. What the heck do I use for f, g, and f + g? I have no idea how to solve this particular problem.

3. "Use a graphing utility to graph f, g, f + g in the same viewing window. Which function contributes most to the magnitude of the sum when 0 (<= less than or equal to sign) x (<=) 2? Which function contributes most to the magnitude of the sum when x > 6?"

f(x) = 3x, g(x) = -x^3/10 (That's -x^3 over 10. Sorry, I just thought I'd be as clear as possible!)

Again I have no idea what they are asking me here. If you could answer just 1 of these step by step that would be great! I would sooooooo appreciate it! And I'm not looking for anyone to do my homework for me, I'm just really confused! Even if you could show be an example step by step for one of these that would be wonderful. Thanks!

Answer
Hello Amy,

1. (a) (f+g)(x) is short for f(x)+g(x), so...
------ (f+g)(x)=x/(x+1) + x^3
---(b),(c), and (d) are similar...(f-g)(x)=f(x)-g(x)
--- (fg)(x)=f(x)g(x), and (f/g)(x)=f(x)/g(x)...OK?

2. See above...

3. See #1...

Let me know if you need any more help...Have Fun!  ;->

Abe