Question

What is the domain of the function y=log(x^2 +4x +3)?

Answer 1

you know that a log must be greater than 0.

Answer 2

When you say, \(\large\color{slate}{ y=\log(a) }\) ,

\(\large\color{red}{ \log(0) }\) is undefined, so must be that: \(\large\color{slate}{ a>0 }\)

what is a in your case?
At what value of x, is it greater than 0?

Answer 3

i would do this right x^2 +4x+3 > 0
and find the solution set?

Answer 4

yes,

Answer 5

correct.

Answer 6

\(\large\color{slate}{ x^2 +4x+3 > 0 }\) try to factor the left hand side.

Answer 7

so the solution would be x<-3 and x>-1

Answer 8

yes, correct.

Answer 9

Ok Thank you

Answer 10

yw