# Composition of Functions

1. Mar 22, 2012

### plzen90

1. The problem statement, all variables and given/known data

Define Function f: [0,1]x[0,2∏)→ℝ2 by

f(r,θ)=

(r(2+cos5θ)cosθ)
(r(2+cos5θ)sinθ)

Let g: [0,2∏)→[0,1]x[0,2∏) be defined by

g(t)=

(1)
(t)

Compute the function δ=f°g, what are the domain and codomain of δ?

2. Relevant equations

3. The attempt at a solution

Replacing r with 1 and θ with t gives

(2+cos5t)cost
(2+cos5t)sint

but this doesn't seem right
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Mar 22, 2012
2. Mar 22, 2012

### Karamata

First, did you mean $f(r,θ)=(r(2+cos5θ)cosθ,r(2+cos5θ)sinθ)$ and $g(t)=(1,t)$?

Look at picture (attachment), and mark the function and you will see

P.S. It seems well.

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3. Mar 22, 2012

### plzen90

yes, thats what I mean.

thanks for the help

I don't really understand the picture, but would the domain be the possible input of g, and the codomain the possible outputs of f?

ie domain of [0,2∏) and codomain of ℝ2 ?

Last edited: Mar 22, 2012
4. Mar 22, 2012

### plzen90

ahh I get your picture now, I think I am right with the domain and codomain?

5. Mar 22, 2012

### Karamata

Yes you are.

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