I have a few questions on composite functions:

Consider 2 functions, f & g.

1. Explain why the domains of f and g must be the same in order to +, - or x the functions.

2. Explain why the domain of f is the range of g for f(g(x)).

3. Let f = { (0,1) (1,3) (2,5) (3,7) } and g(x)=2x+1 ... Evaluate:

a. (g ○ f )(0)

b. (f ○ g)(2)

c. (g ○ f)(3)

Thank you!