Question

Chosen answer is wrong, please help!

Answer 1

x ≠ 8

Explanation:

(
`(f)/(g)` )(x) =
`(f(x))/(g(x))` =
`(2x+5)/(x-8)`

The denominator of (
`(f)/(g)` )(x) cannot be zero as this would make (
`(f)/(g)` )(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x - 8 = 0 ⇒ x = 8 ← excluded value

Thus

domain is all values of x ∈ R , x ≠ 8

Answer 2

A

Explanation:

So we have the two functions:

`f(x)=2x+5\text{ and } g(x)=x-8`

And we want to find (f/g)(x).

This is the same as:

`((f)/(g))(x)=(f(x))/(g(x))`

So, substitute (2x+5) for f(x) and (x-8) for g(x). So:

`=(2x+5)/(x-8)`

Now, we want to find the domain.

Note that this is a rational function. The domain of a rational function is always all real numbers except when the denominator equals 0. This is because, remember, you can't divide by 0!

So, to find the domain restrictions, set the denominator equal to 0 and solve for x. So:

`x-8=0`

Solve for x. Add 8 to both sides:

`x\\eq8`

So, our domain is all real numbers except for 8. We can check this, when x is 8, our function is 21/0, which is undefined.

Therefore, our answer is A.

And we're done!

Edit: Typo