Question

Could someone help me on this problem, I'm a bit lost on it. I know how to do problems like these, but I'm still not understanding what my answer should be.

Question:
Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).

Answer Choices:
A) −7
B) -3
C) 10
D) 33

Answer 1

@Nnesha @nincompoop @dan815

Answer 2

Do you know how to get f(g(x))?

Answer 3

Or to get g(f(x))

Answer 4

Yes, you would have to plug in the 2 for both f(x) and g(x). For both equations.

Answer 5

Alright, good. I just learned these a month ago, so I am no pro, but I will try to help you the best I can. :-) I am fairly good with these.

Answer 6

Would you like me to show you my work and then you could correct me on any mistakes I made?

Answer 7

Question:
Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).

Answer Choices:
A) −7
B) -3
C) 10
D) 33

Okay, so it is saying f(g(2)), which is like f(g(x)), so we should probably try to find that first.

Answer 8

If you want, sure :)

Answer 9

Alright haha.
So, we'll start with g(x) first.
You'd plug in the 2 for all of the x variables.
g(2) = (2)^2 - 6 (2) -7
You'd then simplify:
g(2) = 4 - 12 - 7
You'd then simplify again:
g(2) = -15 ??

Answer 10

I see I'm having trouble with it if it's not even an answer choice lol.

Answer 11

Well, I could see where you are going with. But thats not how we solve for these problems, because they want f of g of x. So, we have to combine f(x) and g(x), THEN we can substitute what f(g(2)) is :-)

Answer 12

Question:
Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).

we have x+8 and x^2-6x-7. we have to multiply the polynomials together in order to get f(g(x)).

Answer 13

(It seems confusing at first, I used to do what you are doing!)

Answer 14

So f(g(x)) will be
x+8(x^2-6x-7))

Answer 15

Let me multiply these real quick

Answer 16

Okay, also, you'd substitute the variables for 2 correct? I want to make sure that's correct at least.

Answer 17

We will not substitute in f(g(2)) until we combine the polynomials. But you will substutute that in :)

Answer 18

First, we need to multiply them together to make it just one polynomial instead of having f(x) and g(x), cause it wants f(g(x))

Answer 19

I am combining them now :)

Answer 20

Oh okay, so how would we do that?

Answer 21

Oh okay, take your time.

Answer 22

I only have one hand to do this cause I injured my other but I will help you, no worries :)
Okay, so we have the two polynomials of x^2-6x-7 and x+8

Answer 23

What we want to do is multiply them together

Answer 24

This will give us the polynomial we need to solve for f(g(2))

Answer 25

Because it starts with f(g(x)), with is f(x) x g(x), basically. Make sense?

Answer 26

Yes, they're both just combined together correct?

Answer 27

If it was just g(x), we would just solve for g(2), but it wants f(g(2)).

Answer 28

Through multiplicaton, yes.

Answer 29

After we combine them, we should get x^3-6x^2-7x-56, if my calculations are correct.

Answer 30

This will be our f(g(x))

Answer 31

So f(g(x))=x^3-6x^2-7x-56.
NOW, try plugging in the 2.

Answer 32

Could you actually tell me how you combined them together before we actually get into the problem? I want to make sure I do it correctly next time haha. :) If you don't mind.

Answer 33

Certainly! Glad you want to learn.

Answer 34

First, set up x^2-6x-7 and then multiply it by x+8. We will start multiplying x^2-6x-7 by 8, just like we would regurlar multiplication. That will give us 8x^2-48x-56 (I actually just caught myself on a mistake, glad you wanted me to show you!)
THEN we will mulitply by the 'x' term of x+8. Put a 0 under our 56 in the above term, multiply out by the same function. We will get x^3-6x^2-7x. NOW lets combine tem (Which I didn't do, oh goodness.)
Drop everything down, we will get x^3-6x^2-41x-56.
This should be the correct formula now.

Answer 35

Wait, x^3-2x^2-41x-56. My bad.

Answer 36

Let me go over my stuff, just to make sure I am right. Before I substitute in.

Answer 37

Cause I think I went wrong somewhere, I confused myself with not adding my terms. Lol I am sorry!

Answer 38

Hmm, I'm still lost on that, I'm sorry. So for the first equation x^2-6x-7, what do you mean by when you multiplied it by x + 8? How would you do that with another equation? I wrote down your steps by the way.

Answer 39

It's okay lol, I'm glad you're trying to help me so we both can understand lol.

Answer 40

Say you have f(x)= x-10 and g(x)=x^2+5x-2. We would multiply them together, so take x^2+5x-2 times x-10. which would yield x^3-15x^2-48x+20. That would be f(g(x)

Answer 41

Okay, I know where I WENT WRONG haha it just dawned on me. Calculus fried my brain.

Answer 42

We want to find f(g(x)). WELL in order to do that, pretend that g(x is a number.

Answer 43

When we have a number for 'x', we just substitute it in for where ever 'x' is.

Answer 44

So when we want to find f(g(x)), we just put g(x) into 'x' for f(x)

Answer 45

My apologizes for confusing you any, however applying and combining polynomials through multiplication is a good concept that should always be learned.

Answer 46

lets go back to our equations we have.

Answer 47

No wonder why my answer was completely off. Lol I will get you the answer now.

Answer 48

Question:
Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).

soo for f(g(x)) our 'x' for f(x) should be g(x). Right?

=x+8 then we will have x^2-6x-7+8 because we are substituing in g(x) for 'x' in f(x).

Answer 49

x^2-6x+1 is now our f(g(x))

Answer 50

NOW we can solve for f(g(2)).
x^2-6x+1 = 2^2-6(2)-1 = -7.

Answer 51

Question:
Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).

Answer Choices:
A) −7 <----- This is the answer
B) -3
C) 10
D) 33

Answer 52

I was thinking of something else and got too caught up in what I said. I am going to delete what I said because its irrelevant to this question particularly.

Answer 53

Or I'll leave them, since you wanted notes. Anyways, when given any function of f(g(x)) or g(f(x)), it is basically saying to substitute in the equation into for 'x'. We could try reversing to see if you understand?

Answer 54

Sorry, I'm reading everything over so I understand, just a moment lol.

Answer 55

You're fine. I'm sorry if I confused you any, I made a mistake in my understanding and started doing another concept, when all we had to do was substitute in g(x) for 'x' in f(x).

Answer 56

Oh yes, let's try the reverse to see if I understand it more as well lol.

Answer 57

Okay this time I won't mess us. Promise. Do you still want to use 2 as our subsituting variable?

Answer 58

*up

Answer 59

Well, wouldn't we use 2 because that's the number given? What other number could we use?

Answer 60

You could use any number, unless they give you a number like they did with f(g(2)). We will still use 2.
Lets state the functions
Question:
Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).
f(x)=x+8 g(x)=x^2-6x-7.
g(f(x))
We will put in f(x) for the variable 'x' in g(x) ; meaning where it shows x squared, x+8 will go there. Remember, though, that we will perform whatever function to the variable being put in, as if it was a whole number such as 2.

Answer 61

Now g(f(x)) will be g(x+8)= (x+8)^2-6(x+8)-7. See?

Answer 62

Oh, because that's f(x) polynomial?

Answer 63

So what you're doing it sticking f(x)'s polynomial into the g(x) one. I was so confused. xD No I understood what you were doing.

Answer 64

Exactly, and for g(f(x)), we use x+8 as the variable. Like how you were putting in '2' for 'x' for g(x), before we put in '2' for g(f(x)), we need to find g(x+8), to get g(f(x)).

Answer 65

Yes. I should have wrote it like I just did. My bad

Answer 66

When we had f(g(x)), we had f(x^2-6x-7) into our x+8.

Answer 67

x= x^2-6x-7. Then we have x^2-6x-7+8.

Answer 68

Combine any like terms, which the only ones is the -7 and 8, which when added give us 1.

Answer 69

Why wouldn't you add the x as well? When you added on just the + 8?

Answer 70

Then we got x^2-6x+1.

Answer 71

Because that 'x' becomes x^2-6x-7. It's like a number. Lets say g(x) just equaled 7. We wanted to find f(g(x)). So, f(7)= 7+8, we don't add or multiply the 'x' to the 7, do we? No. We are just substituing in. That is all. However, if that 'x' was squared, we would of had to of squared the polynomial. Just like if it was x^2+8, and f(g(x))= f(7). We would then have 7^2+8, because that is the nature of 'x'.

Answer 72

Its just like having a numerical variable. Just substitute it in for 'x', you don't need to add or do anything, unless it is squared or possbily cubed, which I haven't encountered cubing yet.

Answer 73

Then you would just square it, and then go on with your calcualtions.

Answer 74

But that isn't the case for this, so we don't need to worry about it. :-)

Answer 75

I hope that helps you out and makes sense. That's the way my Calculus professor taught us.

Answer 76

Sorry.

Answer 77

My sister needed to do something on the computer, I'm so glad you're not gone yet lol.

Answer 78

It's okay! Do you have other problems or any other questions? I love helping with these.

Answer 79

Let me read what you had said before lol, just a second. Then we can go over another one. :)

Answer 80

Alright. I gave you a medal for working with me, even though I was wrong at first. But, that is the joy of math. :-)

Answer 81

Lol, I will give you one as well! You've been a great help. One last question, then I'll close this one and tag you in another one. :)

So, this would be the final equation: x^2 - 6x - 7 + 8 ??
What would I do next, because I now know what you did. Do I substitute 2 into the variables and then it should come out to -7 ??

Answer 82

Yep! You can plug it in and see for yourself. We now know what f(g(x)) equals, so we can find what it equals with '2'.

Answer 83

Omggg, I see it lol. I did the calculations. I feel so great about the problem now. I was very confused!

Answer 84

Because then it becomes f(g(2))=x^2-6x-7+8. With 2^2-6(2)-7+8.

Answer 85

Isn't it the best feeling figuring it out? :)

Answer 86

Yes, instead of just asking for the answer. xD Anyways, I'll close this problem, then we'll go over another one. :) Thank you for helping me with this one!

Answer 87

Okay, perfect. Not a problem, glad to help :-)