Help with Understanding Composite Functions

[frozenbananas]

Homework Statement

posted in title

Homework Equations

none

The Attempt at a Solution

f+g would be

(2x^2+1) + (x-1) = 2x^2 + x so the domain for f+g is all real numbers but i don't know how to find the one for the composite. i am still confused as to what a composite function is, please help me! thank you!

 

[rock.freak667]

composition of f&g is nothing but f o g which is the same as fg or f(g(x)).

So take the entire g(x) and put it wherever you see 'x' in f.

 

[frozenbananas]

the composite is simply g then? or is it f(x) multiplied by g(x)?

 

[danago]

the composite is simply g then? or is it f(x) multiplied by g(x)?

As rock.freak said, it is f(g(x)), not g(x). 'x' is the input to g and then the output g(x) becomes the input to f. It is different to multiplying.

As an example: If g(x)=x+x^2 and f(x)=2x, then the composition gf(x) = 2x + (2x)^2