Question

Is this correct? The quotient of f(x)= x-3 and
g(x) = x-5 is 3/5 and the domain is [5, infinity)?

Answer 1

The quotient should just be (x-3)/(x-5), since if we sub in x =1, we get (1-3)/(1-5) which equals -2/-4 and that is 1/2. So it wouldn't be 3/5.

As for the domain for either of the functions, x should be all real values.

Answer 2

it will be 2.. for domain\[-\infty \to +\infty\] if f(x) is divided by g(x)

Answer 3

x can't equal 5

Answer 4

x can equal 5, it would just mean that f(5) = 0.

Answer 5

If x = 5 you would have 2/0 which is not possible

Answer 6

because zero can't be in the denominator

Answer 7

Wait, aren't they two separate functions?

Answer 8

Oh my mistake, she was looking for the function of the quotient, not f(x) or g(x).

Yeah, x cannot be 5

Answer 9

so for interval notation is it \[[-5,\infty)\]

Answer 10

That's only part of the solution

Answer 11

actually...

Answer 12

i mean \[[5,\infty)\]

Answer 13

(-infinity, 5), (5, +infinity)

Answer 14

That's the solution

Answer 15

the quotient is equal to 1

the remainder is equal to 2

(x - 3)/(x - 5) = 1 + 2/(x-5)

Answer 16

so is it a union for the domain?

Answer 17

yes

Answer 18

sorry, i didn't mean to post that so many times.

Answer 19

and this is all in parenthesis?

Answer 20

yes, correct because 5 is not included in the solution.

Answer 21

how do you know that the domain is a union and not one single set of intervals?

Answer 22

Because the solution is incomplete without the other set. Providing only one set is incomplete.

Answer 23

When you are providing a solution, you have to provide the complete solution.

Answer 24

ok, i think i got it. it's basically saying that the domain is negative infinty, not including 5, and 5 to infinity

Answer 25

Precisely

Answer 26

thank you :)

Answer 27

R\{5} is probably the most succinct way to write the domain using set notation

Answer 28

okay, my teacher hasn't taught that yet, i'm not sure if she will, so i'll just use a union.