1. ## Composite Functions

Hi,

I am perfectly able to understand composite functions, given expressions for each function. Such as f(x) = x + 3, g(x) = 2x +1. Then f(g(x)) would be:
(2x+3)+1 = 2x +4. Am I right?

However, I don't know how to approach questions where only the elements in a function are stated. Like the following:

Given A = {1, 2, 3, 4}, B = {a, b, c, d}:

f(x) = {(1,b), (2,c), (3,d), (4,a)}
g(x) = {(a,1), (b,2), (c,4), (d,4)}

Find g(f(2)) and f(g(2)).

Or rather, what does g(f(2)) and f(g(2)) mean?

2. ## Re: Composite Functions

Originally Posted by aprilrocks92
I don't know how to approach questions where only the elements in a function are stated. Like the following:
Given A = {1, 2, 3, 4}, B = {a, b, c, d}:
f(x) = {(1,b), (2,c), (3,d), (4,a)}
g(x) = {(a,1), (b,2), (c,4), (d,4)}

Find g(f(2)) and f(g(2)).
Or rather, what does g(f(2)) and f(g(2)) mean?
Look, at the definition $\displaystyle (2,c)\in f$ or $\displaystyle f(2)=c.$

Then $\displaystyle g(f(2))=g(c)$ but $\displaystyle (c,4)\in g$ so $\displaystyle g(c)=4$.

Therefore $\displaystyle g(f(2))=4$

Did you copy the problem correctly? Because $\displaystyle f(g(2))$ is not defined.

It could be $\displaystyle f(g(c))~?$