Question

This is a discussion question with several parts that I must answer for my class. I am wondering if anyone can help me with this, as I have no clue what to do and am very confused. I did get the first part done, explaining the composite functions, but the rest is still left unanswered
1. Explain composite functions.
2. For the following two functions answer questions 2a and 2b.

f(x) = x²
g(x) = 2x + 1

2a) Is composite function (g º f) the same as composite function (f º g)?

2b) Evaluate (g º f) for x=2.

3. For your classmates to practice, provide a similar exercise.

Answer 1

If you understand what a composite function, you should have no trouble showing how to find a composition of two given functions.

Let's see an example. Let \(\color{red}{f(x)=x^2}\) and \(\color{blue}{g(x)=\sqrt{x+1}}\). Then \(f\) composed with \(g\), written \((f\circ g)(x)=f(g(x))\) is
\[\color{red}f(\color{blue}{g(x)})=\color{red}f(\color{blue}{\sqrt{x+1}})=\color{red}(\color{blue}{\sqrt{x+1}}\color{red}{)^2}=x+1\]

Answer 2

Does this make sense?

Answer 3

Sort of and sort of not.

Answer 4

Alright, what parts do you (not) get?

Answer 5

all the symbols and letters are throwing me off.

Answer 6

I dont know how to create that type of problem using the functions provided by the teacher. I dont even understand how to lay it all out. This stuff is extremely confusing for me.

Answer 7

I do not much like the little circle notation. Maybe you would find it easier if you used the nesting notation (but you would have to translate back, because there is no guarantee you teacher knows nesting notation.

So 2a becomes is g(f(x)) the same as f(g(x))?

Answer 8

No they are not the same, right? And then how to lay out the problem for 2b?