Question

Let g(x)=log5(x^2+3x-18). Find the domain of g(x).

Answer 1

Is that base 5 or base 10?

Answer 2

base=5

Answer 3

Here, you have to think about what x-values can, mathematically, be used in the function. For logs you can't have negative numbers or 0 so you have to figure out what values of x DON'T give you a negative log.

Answer 4

First, try splitting the polynomial up: x^2 + 3x - 18 = (x + 6) (x - 3)

Answer 5

So, x can't be either -6 or three because that value gives you 0

Answer 6

so it would be (-infinity, -6) U (3, infinity) ?

Answer 7

Exactly.

Answer 8

Yes

Answer 9

Good job!

Answer 10

Yes it is

Answer 11

Change parenthesis to ( ] [ )?

Answer 12

I think -- because with positive three you're adding the 3x instead of subtracting it

Answer 13

Sorry, I made a sign error. It is correct.

Answer 14

Nope, you want open brackets because you can't take the log of 0 and for x = -6 and 3 it is a log of 0

Answer 15

No, the parentheses are correct.

Answer 16

Oh, okay.

Answer 17

Just making sure