Question

What is the domain of

x^2-x-6
---------------
x^2-9x+18

Answer 1

Domena is a set of arguments , the value x.

We need to reject SUCH values ​​of x , which must not be used . We know that you can not divide by zero , so the denominator can not equal zero.

We compute what value of x will give us the denominator 0

x² - 9x + 18 = 0
a = 1 , b= -9 , c=18 - coefficients
discriminant of a quadratic equation

Δ = b² - 4*a*c = (-9)² -4 * 1 * 18 = 81 - 72 = 9 ⇔ √Δ = 3

zeros of functions


`x_(1) = (-b - √(delty) )/(2*a) = (-(-9) - 3)/(2* 1) = (9 -3)/(2) = 3 \\ \\ x_(2) = (-b+ √(delty) )/(2*a) = (-(-9) + 3 )/(2*1) = (12)/(2) = 6`

D = R/ {3,6}