Question

Please help me find the Domain

Answer 1

f(x) = x^2 − 8x + 15
g(x) = x − 3
h(x) = f(x) ÷g(x)

Answer 2

h(x)=5

The domain of h(x) is ____ U _____??

The options for the first part are,
(3,5)
(-infinity,3)
(-infinity,-3)
The options for the second part are,
(3,infinity)
(-3infinity)
(5,infinity)

Answer 3

Factorise f(x) first.

Answer 4

f(x)=(x-3)(x-5) @thomas5267

Answer 5

So what does \(f(x)\div g(x)\) equal to?

Answer 6

h(x)=f(x) ÷ g(x)
h(x)= 5
@thomas5267

Answer 7

=x-5 sorry

Answer 8

If g(x)=0 then f(x)/g(x) means f(x)/0, which is undefined. The domain of h(x) is defined as the largest set of values such that h(x) is defined. What is the domain of h(x) then?

Answer 9

so that would mean that h(x) is undefined but that isn't one of the options on assignment.
@thomas5267

Answer 10

h(x) is undefined only when g(x)=0. When is g(x)=0?

Answer 11

when you factor g(x) it is unfactorable, so idk :/
@thomas5267

Answer 12

g(x)=x-3
x-3=0

Answer 13

so x=3?
@thomas5267

Answer 14

Yes. Actually I don't know whether factoring f(x) is necessary.

h(x) is not defined at x=3. What is its domain?

Answer 15

I have no idea. When I factored f(x) I got (x-3) and (x-5). When I factored g(x) it said it was undefined. When I divide f(x) from g(x) I get x-5 but when I try to find the domain for x-5 I cant get any of the answers that are in the options for the assignment, I always get (-infinity, infinity)

Answer 16

g(x) is defined for all real numbers and so is f(x). However, 1/g(x) is not defined at g(x)=0 (x=3) 1/g(x) at x=3 means that 1/0, which is undefined.

Answer 17

okay so we know that g(x) is undefined

Answer 18

I feel like we have everything we need to find the domain I just don't know how to get that @thomas5267

Answer 19

The domain is (-infinity,3)U(3,infinity) as the only point h(x) is not defined is x=3, which corresponds to g(x)=0.