Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

Yep

Answer 5

So does that mean it is 8 or 16?

Answer 6

Wait a minute.

Answer 7

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

Answer 8

Ugh...

Answer 9

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

Answer 10

Which part is confusing you exactly?

Answer 11

So 16 = 9+6+1 is correct?

Answer 12

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

Answer 13

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.

Answer 14

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

Answer 15

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.

Answer 16

N...No?

Answer 17

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

Answer 18

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

Answer 19

Do you see it now?

Answer 20

the +1 you can add up at the end

Answer 21

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

Answer 22

+2?

Answer 23

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

Answer 24

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

Answer 25

Alright.

Answer 26

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

Answer 27

Okay.

Answer 28

So what is the first step you would do?

Answer 29

= 125 - 15 + 5?

Answer 30

Let's check

Answer 31

Sorry -125

Answer 32

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

Answer 33

Did you get -125 - 15 + 5?

Answer 34

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

Answer 35

Alright :D and that gives you -135 correct?

Answer 36

yes

Answer 37

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 \(f(-5)\)

Answer 38

So then what is -135 + 3?

Answer 39

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

Answer 40

*-132

Answer 41

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

Answer 42

Alright. Thank you so much for all your help!