functions defined

Question

f(1)=2

f(7)=10

f(12)=3

 

g(1)=4

g(7)=17

g(12)=9

 

a. (f/g)(1)=

b. (f/g)(7)=

c. (f/g)(12)=

d. Is f/g a function? Use the definition of a function to explain

e. What is the domain of f/g?

f. What is the range of f•g?

 

Answer 1

a)

 

(f/g)(1) = f(1) / g(1)

            = 2 / 4

            = 1/2

 

(f/g)(7) = f(7) / g(7)

             = 10/17

 

(f/g)(12) = f(12) / g(12)

              = 3 / 9

              = 1/3

 

d)

 

In order for f/g to be a function, the values of (f/g)(x) must have only one value of x.  In other words, no more than 1 value of (f/g)(x) can share the same x value.

 

Each x value has a different output value.  Therefore, f/g is a function.

 

We can put this in a table.

 

x  |    f/g

__________

1           1/2

7          10/17

12         1/3

 

 

e)

 

Domain is the set of x value in which a function is defined.  Domain of f/g is

 

x {1, 7, 12}

 

 

f)

 

Range is the set of y values in which a function is defined.  Range is then,

 

y = {fg(1) , fg(7) , fg(12)}