Question

Help with this function. PLEASE. The function H is defined below
h(x)=x+3/x^2-64
Find all the values of x that are not in the domain of h.

Answer 1

\[h(x)=\frac{x+3}{x^2-64}\]
@maddiemaze The values of x for which h(x) becomes undefined are not in the domain.
Do you have any idea, how we should proceed?

Answer 2

No

Answer 3

OK, if you put x=8 , what would you get for h(x)?

Answer 4

8h

Answer 5

\[h(x)=\frac{x+3}{x^2-64}\]
x=8
\[h(8)=\frac{8+3}{8^2-64}\]
Can you try to solve the left side?

Answer 6

11/0

Answer 7

Good :)
\[\frac{11}{0}=\infty\]
Which is undefined, so if the denominator becomes 0, then h(x) would be undefined.
@maddiemaze is there any other value of x for x^2-64=0??

Answer 8

if its undefined than I dont think there would be another value

Answer 9

Solve for
\[x^2-64=0\]
It's a quadratic, it'd have two values of x

Answer 10

8

Answer 11

and the other one?

Answer 12

I have no idea

Answer 13

\[x^2-64\]
\[x^2-8^2=0\]
We know
\[a^2-b^2=(a+b)(a-b)\]
so

\[(x+8)(x-8)=0\]
\[x=8, -8\]

Answer 14

so kind of like absolute values?

Answer 15

Yes, so the domain would be all real no.s except (8, -8)

Answer 16

Do you understand?

Answer 17

yes thank you for help :)