Answer:
DOMAIN : x ∈ (-∞ , -3 )U (4 , ∞) or {x | x ∈ R where x ≠ -3 and 4}
REAL ZEROS : x = 5/3
Step-by-step explanation:
[tex]f(x) = \frac{3x -5}{x^{2} -x-12}[/tex]
factorize the bottom part
[tex]x^{2} - x - 12[/tex]
product = -12 , sum = -1 , factors = -4 and 3
[tex]x^{2} +3x-4x-12=0[/tex]
x (x + 3) - 4(x + 3) = 0
(x - 4) ( x + 3) = 0
x - 4 = 0 and x + 3 = 0
x = 4 and x = -3
for the function f(x) the domain is all real numbers ( R ) except - 3 and 4
Domain = x ∈ (-∞ , -3 )U (4 , ∞)
TO FIND THE ZEROS LET f(x) be equal to zero
[tex]0 = \frac{3x - 5}{x^{2} - x - 12}[/tex]
cross multiply
0 = 3x - 5
find x
3x = 5
[tex]x = \frac{5}{3}[/tex]
