domain of 6x^2-3x/x^2-x-42

Question

how do i get the domain of them f/g

 

Answer 1

If  f(x) = 6x^2 - 3x  and  g(x) = x^2 - x - 42  then the only restriction on the domain of f/g is that g cannot equal 0.  To find where g = 0, set g(x) = 0 and solve for x  

 

x^2 - x - 42 = 0

(x - 7)*(x + 6) = 0

x - 7 = 0  or  x + 6 = 0

x = 7  or  x = -6

 

So the domain of f/g is all real numbers except x = 7 or x = -6  

You can write this in interval notation as (-∞,-6) U (-6,7) U (7,∞)