Question

Find the domain and real zeros of the given function
F(x)= 3x-5/x^2-x-12

Answer 1

DOMAIN : x ∈ (-∞ , -3 )U (4 , ∞) or x

REAL ZEROS : x = 5/3

Explanation:

`f(x) = (3x -5)/(x^(2) -x-12)`

factorize the bottom part

`x^(2) - x - 12`

product = -12 , sum = -1 , factors = -4 and 3

`x^(2) +3x-4x-12=0`

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

`0 = (3x - 5)/(x^(2) - x - 12)`

cross multiply

0 = 3x - 5

find x

3x = 5

`x = (5)/(3)`