Melody

Thanks RainbowPanda  

Thanks Heureka. That is great !!

Did you actually read any of what we wrote?

My answer came in one minute after yours. I was working on it before you said you could do it.

You had not said that you already understood otherwise I would not have wasted my time.

You have done this too many times RP.  

Do not ask questions until you have given youself lots of time to think about it first. !!

If you do not need to ask then do not ask.

If anyone puts their time into giving you an answer then ALWAYS give feedback and say thank you.

\({x(x+1) \over 4x^{2}+6x+3}   \)

You cannot divide by 0 so the denominator cannot be 0

\(x \ne {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x \ne {-6 \pm \sqrt{36-48} \over 8}\\ x \ne {-6 \pm \sqrt{12} \;i\over 8}\\ \)

This is a complex number so there are no restriction on x in the real number system.

There answer has restricted values but I do not think that this is what the question is asking.

Here is the graph if the expression was put equal to y.

You can see that the range is quite restricted.   The domain is not restricted.

Hi Heureka,

I am wondering if it can still be done easily if it is made more complicated ?

eg

Find the coefficient of x^3 y^3 z^2 in the expansion of (3x+5y+7z)^8.

Yes, that does sound like a good analogy.     :)

Thanks Heureka, I can't remember ever seeing this type of solution before. 

So I am very pleased that you have shown me.   

LOL   That is a lot of butting in    

Do I have to demerit myself as well since I butted in too ?

RP does not seem to need our help anyway she nearly always say she is desperate for help and then works it out within minutes by herself.   

This forum must teach by osmosis LOL 

Please no one else butt in because I actually want to help RB to understand.

Hi RB,

I like the way tyou said that.

I often say, I understand ... but ... I don't really understand.  

There  are different levels of understanding in mathematics.

Let's see if I can help.

I'll do the first one and then you can try the others.

1)  \(f(x)=2x-5\qquad find\;\;\quad f(6) \quad and \quad f(1)\)

For  f(6) you are replacing all the x'es with 6

so

\(f(6) = 2*6 - 5 = 12-5 = 7\)

-------------

For   f(1) you are replacing all the x'es with 1

so

\(f(6) = 2*1 - 5 = 2-5 = -3\)

NOW you have a go at at least one of the other questions. show me your working, and I will see if I can help you get to the point of  REALLY understanding       

Lightning, if someone responds to your question it is polite for you to respond.

A thank you and also a point is always appreciated but if you do not understand or you need more help, or even if you think the answer is wrong, then please interact with the answerer!!