Functions and Composition of functions

Question

Let f be a function whose domain is {1,7,12} and such that f(1)=2, f(7)=10, and f(12)=3. Let g be a function whose domain is {3,7,20} and such that g(3)=-9, g(7)=31, and g(20)=60.

 

1. What is the domain of g º f?

2. What is the range of g º f?

Answer 1

The domain of g(f(x)) must use input f(x) values that belong to the g-domain, namely 3, 7 or 20.

The only f(x) value that is an output agreeing with this list is 3, which traces back to f(12)=3.

 

Therefore the domain of gΟf is just 12.

The range is g(f(12)) = g(3) = -9, only.