Domain, Range, Composition of Functions

Question

Let f be a function whose domain is the set {1,7,12} defined by:

 

f(1)=2

f(7)=10

f(12)=3

 

Let g be a function whose domain is the set {3,7,20} defined by:

 

g(20)=60

g(7)=31

g(3)=-9

 

a. What is the domain g º f?

b. What is the range of g º f?

Answer 1

a. What is the domain g º f?    g(f(x)) for x=1, 12 or 7, the f values are 2, 3, 10, respectively.

 

Those f values are required to be in the domain of g, so only f(12) = 3 makes the grade!  ANSWER: {12}

 

b. range of g º f?  just g(f(12) = g(3) = -9.  ANSWER: {-9}