Determine all non permissible values

Question

Determine all the non-permissible values of 

 

f(x)= (x^2-1)/(x^2-x-6)

Answer 1

 

              (x² - 1)

f(x) = ---------------

           (x² - x - 6)

 

We can factor the numerator and denimimator

 

           (x - 1)(x + 1)

f(x) = ------------------

           (x - 3)(x + 2)

 

We must exclude from the domain, all values for x that cause division by 0 (undefined).

 

We can set the denominator equal to 0, and solve to getthos excluded values.

 

Using the Zero Product property,

 

    (x - 3)(x + 2) = 0

 

    x - 3 = 0        or    x + 2 = 0

    x = 3                    x = -2

 

Thus we must exclude -2 and 3 from the domain of the function.