Question

Let f(x) = x - 2 and g(x) = x^2 - 7x - 9. Find f(g(-1)).

Question 8 options:
1) -21
2) -3
3) 3
4) 21

Answer 1

hello joemath

Answer 2

yo :)

Answer 3

guess what i had a huge "discussion" about two days ago

Answer 4

what? o.O

Answer 5

@marc
\[g(-1)=-1\]
\[f(-1)=-3\]

Answer 6

here is a hint. what is
\[\sqrt{16}\]?

Answer 7

LOLOL

Answer 8

First, work out what g(-1) is. In the equation \(g(x) = x^2-7x-9\), replace the x with -1.

Answer 9

really it went on for ages

Answer 10

you arent serious lolol

Answer 11

guy tried to tell me that
\[f(x)=\sqrt{x}\] is not a function

Answer 12

LOLOL was it Chenna by any chance?

Answer 13

unless you write
\[f(x)=\sqrt{x}:x \geq0\]

Answer 14

lololol

Answer 15

i forget name. i almost gave up

Answer 16

It was me!

Answer 17

i guess people really dont understand square roots, that much >.<
@Dalvoron was it really? o.O you dont seem like someone that would make that mistake.

Answer 18

It's what textbooks tell me, it's what definitions tell me, it's what my lecturers have told me. I still believe it to be true, as I've found no evidence to the contrary, apart from \(\sqrt{x}\) referring only to the principal square root by convention in some cases, but not in others.

Answer 19

There was a problem on here posted a while ago where we abused the fact that
\[\sqrt{x} = |x|\]
let me see if i can find it...

Answer 20

then i have a question. why is quadatic formula
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]? what is the plus or minus there for if the square root can be negative as well?

Answer 21

mabye satellite can find it first, im looking for the piecewise function problem.

Answer 22

i have yet to see a textbook that says
\[\sqrt{a^2}=\pm a\]

Answer 23

because if the square root also returned a negative value i dont think we could have solved it the way we did.

Answer 24

or a text that said
\[\sqrt{16}=\pm4\]

Answer 25

Because the convention sometimes applies there I guess.

Answer 26

have you seen this?
http://www.wolframalpha.com/input/?i=sqrt%28x%29+%3D+-4

Answer 27

convention "sometimes applies"? no the convention always applies. root means positive root. it is the inverse of the function
\[f(x)=x^2: x \geq 0\]

Answer 28

I have a text here (Text & Tests 1) which states "The square root of a number is the number which when multiplied by itself gives the number.", which would apply equally correctly to a positive or negative number.

Answer 29

wow really? then i understand your confusion because if that is what it says, that is what it says. but if you look at the graph of
\[y=\sqrt{x}\] you will see that it exists on the right hand side of the y axis, and only exists on theh left if you allow for complex numbers

Answer 30

its not like i dont see where youre coming from, i was taught that the square root of a number is a plus or minus thing too.
When i got to a analysis class though and got a problem wrong because of it though, i learned why thats not the case (in regards to functions, which is what that problem is about)

Answer 31

For the sake of clarity, I can see why there should be universal acceptance of one or the other, but it just isn't the case. You probably see it more than I do as being only the principal square root, but that doesn't seem to be the case in Ireland.

Answer 32

in fact i am completely baffled because when you derive the quadratic formula for example you start by saying that if
\[x^2=9\] then
\[x=\pm3\] and if
\[x^2=5\] then
\[x=\pm\sqrt{5}\]

Answer 33

if the square root of 5 could be negative, then the plus minus bit is superfluous

Answer 34

As much as I with maths always made sense to me, it doesn't :P Perhaps it's more widely accepted in the world of mathematics, but I studied physics mainly with some mathematics, and never saw that convention.

Answer 35

i will believe you but i find it a bit bizarre that in Ireland the square root function is not well defined

Answer 36

its because mathematics is taught sort of backwards imo. We use things before we truely understand them.

Answer 37

i mean is certainly believe you since you say it. no reason to doubt you. could you send me a reference?

Answer 38

Well when it's referred to as a function, naturally it can only refer to one of the roots, but we don't call it a function outside of the case where we specifically see \(f(x) = \sqrt{x}\), or some derivative of that.

Answer 39

I mean, think about calculus. You start taking derivatives and integrals before you even learn the analytic side which lets you know when you are able to take derivatives and integrals.

Answer 40

backwards!

Answer 41

There was that textbook reference a few minutes ago. I'll try looking through some exam paper marking schemes where we would be penalised for not writing both roots.

Answer 42

i checked here
http://en.wikipedia.org/wiki/Square_root

Answer 43

yes math is always taught backwards. annoying

Answer 44

Let f(x) = x2 - 81. Find f-1(x).

Question 7 options:
1) ± √x+81
2) ± 9√x
3) 1 over x^2-81
4) x^2 over 81

Answer 45

and thats what creates this misunderstanding. You are taught one thing in middle/high school because its easier to grasp, and then taught something else in college.

Answer 46

In the mean time: http://dictionary.reference.com/browse/square+root http://www.thefreedictionary.com/square+root

Bear in mind, they're dictionaries, not mathematical textbooks of course :P

Answer 47

It's unfortunate that I'm going to be a teacher, and I'm going to have to stick with the curriculum, rather than teaching what is "correct". I'd like to teach the use of \(\tau\) rather than \(\pi\) as well, but I can't do that either :(

Answer 48

ahh i see. it seems to say that "square root" could be positive or negative, but that the symbol
\[\sqrt{x}\] means the positive number

Answer 49

That just makes it even more confusing.

Answer 50

so i will admit to being incorrect about the term "square root" but correct in my assertion that
\[\sqrt{x}\] is positive.

Answer 51

thus for example
16 has two square roots,
\[\sqrt{16}=4\] and
\[-\sqrt{16}=-4\]

Answer 52

and will have to stop myself from saying "plus or minus the square root of 16"

Answer 53

im done >.< this is the second time this has come up ( with the same problem no less! lol)

Answer 54

With any luck, that will propagate over here, and the whole issue will not exist in future.

Answer 55

i wonder what i can say instead?

Answer 56

Refer only to the principal square root :P

Answer 57

btw not to beat a dead horse, but the question where this came up had to do with whether
\[\sqrt{10}\] was greater than 3. i maintain that it is greater than three because the root symbol means positive one

Answer 58

in other words i maintain that
\[\sqrt{10}\] is not some number whose square is ten, but the positive number whose square is ten

Answer 59

Fair enough. For the purposes of this site at least, I'll try to make the distinction

Answer 60

beat that dead horse! lol

Answer 61

glad that is cleared up, at least for me

Answer 62

someone give me a medal so i can be lvl 60 lol >.>

Answer 63

nvm, thanks dalvoron :)
and satellite :P

Answer 64

Congrats on hitting 60!

Answer 65

thanks!

Answer 66

@dalvoron am sure you will make an excellent math teacher, and enjoy it too. outside of the vow of poverty you will have to take.

Answer 67

just please don't ask your students ever to "simplify" please please please.

Answer 68

i couldnt fine the piecewise problem :( forever lost!

Answer 69

I'm caught between a rock and a hard place. Ideally, I should teach them about the truth of mathematics, and be as clear as possible; but at the end of the day, they have to be prepared for the exams that come up. Perhaps an educational reform is in order, and I can squeeze in my love of \(\tau\) as well!

Answer 70

do it in secret <.< a secret society of truth!

Answer 71

I could totally do that. Conspire with my fellow maths teachers as well. Write a textbook with subtle references to the truth.

Answer 72

i think i saw it here, maybe, an otherwise excellent video, where he says "simplify" to mean three completely different things. sometimes it means add to get 0, sometimes it means cancel to get one, and sometimes it means that a function composed with its inverse "simplfies" so give what you started with

Answer 73

Every now and then, it becomes apparent that we humans can be really stupid.

Answer 74

if you want a laugh look at the implicit differentiation video here
http://justmathtutoring.com/

Answer 75

I was never great at implicit differentiation, but I think I just got worse.

Answer 76

Let f(x) = 8x^3 - 22x^2 - 4 and g(x) = 4x - 3.

Question 4 options:
1) 2x^2 - 4x - 3 - (13 over 4x-3)
2) 2x^2 - 4x - 3 - (4x-3 over 13)
3) 2x^2 - 7x - 1
4) 2x^2 - 7x - 5 + (x-4 over 4x-3)

Answer 77

marc you should repost this question anew. no one will find it hear. it is also incomplete because we are not sure that to do with f and g

Answer 78

Sorry about highjacking the question, but I think there are some helpful answers in there somewhere.