f(x)=1/x^2-6x-7

Question

find the domain

Answer 1

1/(x²-6x-7)

 

In math, division by 0 is undefined.  So any value of x that makes the denominator of f(x) equal 0 will make f(x) undefined at those points.  The values of x that make f(x) undefined are excluded from the domain of f(x).  So we need to find the values of x that make x² - 6x - 7 equal to zero:

 

(x²-6x-7) = 0

(x-7)(x+1) = 0

 

The values x = 7 and x = -1 make the denominator of f(x) equal to 0.  So the domain of f(x) is all x except x = -1 and x = 7.

Answer 2

The domain in interval notation is

 

 

(-∞, -1)∪(-1, 7)∪(7, ∞)