find the domain of the function fx logx29x18Solutionfx logx2

find the domain of the function.

f(x)= log(x^2+9x+18)

Solution

f(x)= log(x^2+9x+18)

for log function: log(f(x)) ---> f(x) > 0

x^2 +9x +18 >0

x^2 +6x +3x+18 > 0

x( x+6) +3(x+6) >0

(x+3)(x+6)>0

x< -6 or x>-3

Domain : ( -inf, -6) U ( -3, +inf)