f(x)= x2-64/x2-2x-48.

Question

for the following rational function, state the restrictions on variable, if any, by finding all values of the variable that are not in the domain of f. write answer with ≠.

Answer 1

We factor f(x) and then set the denominator equal to zero.

 

f(x) = (x + 8)(x - 8) / (x + 8)(x - 6)

 

The next thing we can do is cancel out terms.  But I warn you.  If you do cancel out terms such as (x + 8), you limit any solutions that you can have.  So we will not cancel out terms. 

 

Set the denominator equal to zero.

 

(x + 8)(x - 6) = 0

 

x = -8        and        x = 6

 

 

so for the function f(x),

 

x ≠ -8         and       x ≠ 6