If g(x) = x2 – 2x, find the value of g(-3) + 1.
Is 8 = 4 + 4 correct?

- Republican31

If g(x) = x2 – 2x, find the value of g(-3) + 1.
Is 8 = 4 + 4 correct?

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- anonymous

If you mean
\[\Large g(x)=x^2-2x\]
then
\[\Large g(-3)+1=(-3)^{2}-2(-3)+1=9+6+1=16\]

- Republican31

Yes sorry that is what I meant. I didn't notice that little formatting error.

- Republican31

But it's -3 + 1, meaning -2, right?

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## More answers

- Jhannybean

Yep

- Republican31

So does that mean it is 8 or 16?

- Jhannybean

Wait a minute.

- anonymous

If you mean
\[g(-3+1)\] then is 8, but if is
\[g(-3)+1\] then is 16

- Republican31

Ugh...

- Jhannybean

\[g(\color{red}{-3})+1=(\color{red}{-3})^{2}-2(\color{red}{-3})+1=\color{red}{9}+6+1=16\]

- Jhannybean

Which part is confusing you exactly?

- Republican31

So 16 = 9+6+1 is correct?

- Jhannybean

Well, when you add 9 + 6 + 1, what do you get?

- Republican31

I just don't understand how (-3) + 1 is any different from (-3 + 1) unless it's because of the g in front. I don't like these functions.

- Jhannybean

Well, think about \(x=-3\) , does that also mean \(x=-3+1\)?

- Jhannybean

Your question is basically saying that you have a function \(g(x) = x^2-2x\), now when \(x=-3\) you replace \(-3\) wherever you see \(x\) in the function.

- Republican31

N...No?

- Republican31

Okay. And then the +1? I see it come in at -2x, but not for the x^2.

- Jhannybean

Ontop of that, you're adding a `+1` to your function's value, therefore \(g(x)+1\) is what you're solving for.

- Jhannybean

Do you see it now?

- anonymous

the +1 you can add up at the end

- Republican31

Okay but why isn't it + 2 for both times that x was used?

- Jhannybean

+2?

- Jhannybean

Okay let's try a different question. Like to try a different one? This time you will solve it.

- Republican31

I'm sorry I just am having trouble understanding. What I'm wondering is if there was
x2 - 2x, then doesn't that mean (-3) + 1 was used twice, so there should be a + 1 from each time x was used in the equation

- Republican31

Alright.

- Jhannybean

Let's take \(f(x) = x^3+3x+5\) and we're finding \(f(-5)+3\)

- Republican31

Okay.

- Jhannybean

So what is the first step you would do?

- Republican31

= 125 - 15 + 5?

- Jhannybean

Let's check

- Republican31

Sorry -125

- Jhannybean

\[f(\color{blue}{-5}) = (\color{blue}{-5})^3 +3(\color{blue}{-5})+5\]

- Jhannybean

Did you get -125 - 15 + 5?

- Republican31

Ya. I saw my mistake of having 125 instead of -125.

- Jhannybean

Alright :D and that gives you -135 correct?

- Republican31

yes

- Jhannybean

Now that we've solved that portion, we're going to add \(+3\) to our answer. This is because we are looking for \(f(-5)\color{blue}{+3}\) and not just \(f(-5)\)

- Jhannybean

So then what is -135 + 3?

- Republican31

Alright but I just was wondering why it isn't (-5) + 3^2. And it's 132.

- Republican31

*-132

- Jhannybean

To my knowledge, we're changing and shifting a function by changing the x value. you `might` be over thinking it!

- Republican31

Alright. Thank you so much for all your help!

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