Find the hole(s), if any for:

Question

f(x)= x^2+3x-54

        -------------

            x^2-36

 

 

A. x=-6

B. x= 2/3

C. x= 6

D. x= 9 

E. x=-9

F. None of the above. 

Answer 1

To find any holes, we need to factor the function f(x).

 

 

f(x) = [(x + 9)(x - 6)] / [(x + 6)(x - 6)]

 

 

Now, we look for factors that cancel each out.  The factor that cancels out is (x - 6).  If we set the factor equal to zero, we get

 

x = 6

 

This is your hole.  x=6 is solution to the function, and at the same time the undefined value.