The function of f is defined below fx x2 6x 7x2 3x 40 F

The function of f is defined below: f(x) = x^2 - 6x - 7/x^2 + 3x - 40 Find all values of x that are NOT in the domain of f. If there is more than one value, separate them with commas. X =

Solution

f(x) = ( x^2 - 6x - 7) / ( x^2 + 3x - 40 )

factoring top and bottom expression

f(x) = ( x- 7) ( x+1) / (x-5) (x+8)

setting denominator not equal to 0

(x-5) (x+8) not equal to 0

x not equal to 5

x not equal to -8

hence domain is all values of x except 5 , -8

X = 5 , - 8