Wednesday

April 16, 2014

April 16, 2014

Posted by **OwlsandOctopi** on Monday, November 21, 2011 at 10:13pm.

Assume that the moving companies are described by the functions

f(x) = 5x and g(x) = 1/x

a. Find a general form for all the functions that you can get by taking

repeated compositions of the two functions.

b. What are all the possible addresses that you can move to? If the list is

infinite, list at least three possible addresses.

I'd be able to find b. if I could just understand a. I'm not quite sure what they're asking for when they want a "general form for all the functions" that I can get from repeated compositions of the two. Just one new function that serves for repeated compositions of both? Or something else entirely?

- Calculus -
**Steve**, Tuesday, November 22, 2011 at 10:56amRepeated compositions seems a bit vague. One way to interpret that is:

(fog)(x) = f(g(x)) = f(1/x) = 5/x

(fog)(5/x) = f(g(5/x)) = f(x/5) = x

So, the functions just swap back and forth between 5/x and x

That doesn't seem too useful.

Another way might mean

f(x) = 5x

f(g(x)) = f(1/x) = 5/x

f(g(f(x))) = f(g(5x)) = f(1/5x) = 1/x

So, now we see that fogof = g

I think you are right in considering that they want a single function, which should follow a pattern of repeated compositions, but I don't see anything useful.

**Related Questions**

calculus - Imagine that you live on an infinitely long and straight street ...

Calculus - Imagine that you live on an infinitely long and straight street ...

7th grade math Ms. Sue please - 1. 2(x – 3) = 2x (1 point) one solution no ...

math - Decide whether each equation has one solution, no solutions, or ...

Physics - Two thin, infinitely long, parallel wires are lying on the ground a ...

PHYSICS - Two thin, infinitely long, parallel wires are lying on the ground a ...

Physics - Two thin, infinitely long, parallel wires are lying on the ground a ...

Physics - Two thin, infinitely long, parallel wires are lying on the ground a ...

English - What do you think Keats means in these lines from "When I Have Fears ...

math :( - No solutions, one solution, or infinitely many solutions??? 2(x – 3...