Please help. Will fan and medal.

Question attached in comments

Question

Please help. Will fan and medal.

Question attached in comments

anonymous · Answer

attachment

rhondasommer · Answer

alright; replace x in f(x) with g(x)

rhondasommer · Answer

brb

rhondasommer · Answer

need to go eat

anonymous · Answer

$$\sqrt{4 * 1/x-4}$$  ?? and okay I'll be here whenever you're ready

dannyo19 · Answer

Did you try graphing f o g?

anonymous · Answer

I don't know how to ._.,

dannyo19 · Answer

substitute g(x) in for f(x)

dannyo19 · Answer

so you have f of g(x)...

anonymous · Answer

Tat's what I was trying to do in that equation above...

dannyo19 · Answer

(that's the function f (g(x)) )

anonymous · Answer

Okay so how would it look the way you are saying? I've never seen it like that before I don't think so I'm not sure what would be substituted where exactly.

mathmale · Answer

Write out f(x) and g(x).

\Throw out the "x" from f(x), on both sides of the equal sign.

Replace it with g(x) = 1/(x-4).   This is your f(g(x)).  Show your work, please.

anonymous · Answer

$$f(x) = \sqrt{4x}   $$     $$g(x)=1/x-4$$

$$f(1/x-4)=\sqrt{4*1/x-4}$$

@mathmale

mathmale · Answer

That x-4 must be enclosed in parentheses for max. clarity.
Please do that.  Combine the 4 and 1 to get 4.

anonymous · Answer

Sooooo $$f(1/x-4) =\sqrt{4/(x-4)}$$  ?

anonymous · Answer

Is that right? :/

dannyo19 · Answer

right

anonymous · Answer

So what now?

dannyo19 · Answer

You can graph that function or analyze it given your possible answers.

dannyo19 · Answer

If x is negative you're going to get complex numbers right?

dannyo19 · Answer

If x is 4 you get a function with a real number divided by zero

dannyo19 · Answer

sqrt of -number will not be found in the domain of the graph amongst the reals

anonymous · Answer

I'm kind of confused by those last three statements ._.,

dannyo19 · Answer

So the Sqrt of 4/ x-4 will have a domain such that x-4 is greater than zero ... Does that make sense to you?

anonymous · Answer

More than before but not fully

anonymous · Answer

Ahh okay. So is 5 the answer?

dannyo19 · Answer

Yeah.   Cuz the square root of a negative number doesn't exist, and neither does the square root of 4/0 in the case of the domain, since you're only dealing with real numbers.

dannyo19 · Answer

Graphing the function would confirm that 5 is the only number on the list in the domain.

anonymous · Answer

Thank you.! Can you help me with some more?

dannyo19 · Answer

Yeah sure.

mathmale · Answer

Please post further questions separately, OK?