Function Operations

Question

I am doing Function Operation in my math class, I was wondering if someone could explain in more detail what a composite function is... Im not sure how to get my answer

Here is a sample problem

f(n)=2n

g(n)=-n-4

Find (f°g)(n)

 

The correct answer is supposed to be -2n-8 but im not sure how to get that

I also am required to state the domain. If someone can explain this too that would be awesome.

Answer 1

The composition of two functions is what happens when you take two functions, run an independent variable through the first (inner) function and the take that result and use it as the independent variable for the second (outer) function.

 

in your example you are taking fog(n) which is pronounced "f of g of n."  This can also be written f(g(n)).

 

take me your beginning n and feed it into g(n)

g(n) = n - 4

 

So now you want to use this value of g, that is (n - 4) as the independent variable for f(n). 

f(n) = 2n

 

so, f(g(n)) = f(n- 4) = 2(n - 4) = 2n - 8

 

 

the domain of f(g(n)) is the domain of 2n - 8, that is all reals.   The domain can be restricted if the range of g(x) produces values that do not cover all reals.  Say, if g(n) only produced positive values, then f(n) = 2n could only double positive values for f(g(n)).