Question

f(x) = 5x + 3; g(x) = 6x - 5

Find f/g.

5x + 3/6x - 5 domain {x|x ≠3/5
or
5x + 3/6x - 5 domain {x|x ≠ 5/6 ?

Answer 1

Do you know how to find the domain?

Answer 2

I'm pretty sure it's the second one because the bottom can't equal to 0 right?

Answer 3

You are correct sir!

Answer 4

Thank you! I just don't want to take chances with picking the wrong one XD

Could you maybe help me with one more question?

Answer 5

Sure.

Answer 6

Find f(x) and g(x) so the function can be expressed as y = f(g(x)).

y = 8/x^2 + 4


I want to say
g(x)= 1/x
f(x)= 8/x +4 but it doesn't look right.

Answer 7

Okay, there are many possibilities for something like this. I would say the easiest way, since it's a fraction, would be to make the denominator an x. and make g(x) whatever is in the denominator

Answer 8

If you plug in what you got we would get this:
\[\frac{8}{\frac{1}{x}+4}\]

Answer 9

Are you with me so far or did I lose you? :/

Answer 10

I'm a bit lost XD
But does this look alright? I think I got it on my own.
g(x)= 1/x^3
f(x)= 8x +4x^3

Answer 11

Hm, well plug it in, where ever you see an x for f(x) plug in g(x)

Answer 12

Because the x's cancel each other out right?

Answer 13

No, you don't keep the x, you plug it INTO the x.

Answer 14

If you had this:
f(3)=x^2-1
What would you do?

Answer 15

Oh. Then carry on XD

Answer 16

3^2-1

Answer 17

Exactly, and f(g(x)) is the same concept, expect you're using equations instead of numbers.

Answer 18

Would it be this simple then?
g(x)= x^2
f(x)= 8/x +4

Answer 19

The simplest way to think of it, like I said earlier was to just separate them into two different equations