Find the requested Function Value and state Its domain

Question

f(x)= 3x+1, g(x)=3x-2

 Find f/g

Answer 1

f(x) = 3x + 1

g(x) = 3x - 2

 

(f/g)(x) = (3x+1)/(3x-2)

 

In math. division by zero is undefined.  So any value of x that makes the denominator of a rational expression equal to zero will make the rational expression undefined.  Such values of x are excluded from the domain.  The denominator of f/g is 3x-2.  Solve the following for x:

 

3x - 2 = 0

3x = 2

x = 2/3

 

The domain of f/g is all x except x = 2/3.  In interval notation (-∞,2/3)U(2/3,∞).