Question

Help me with some questions?

Given f(x) = 6x2 – x – 12 and g(x) = 2x – 3, find the function (fg)(x).

Evaluate the composite function f(g(x)) for x = 31.

Answer 1

Much gratitude to whoever helps me. I just can't get these. I hate alg 2

Answer 2

f + g ?
You just add f(x) and g(x)

Answer 3

would the answer just be x^2? for that one?

Answer 4

As a matter of fact, yes :D

Answer 5

now the composite function f(g(x))
is a little tricky
What you do is replace all instances of x in f(x) with g(x)

Answer 6

\[\large f(\color{orange}x) =2 - \color{orange}x^2\]\[\large \color{red}{g(x)=3x+10}\]
\[\Large f[\color{red}{g(x)}]=2-[\color{red}{g(x)}]^2\]

Answer 7

And then I just solve that?^

Answer 8

replace g(x) and then solve from there, yes :D

Answer 9

okay I get x-5. Is that correct?

Answer 10

I don't think so. Remember
\[\large g(x) = 3x+10\]

Answer 11

hmmm, is it 6x+20?

Answer 12

You're guessing. Replace the g(x) here
\[\Large f[\color{red}{g(x)}]=2-[\color{red}{g(x)}]^2\]
with 3x + 10 like so...
\[\Large f[\color{red}{g(x)}]=2-[\color{red}{3x+10}]^2\]

Answer 13

and carry on from there...

Answer 14

No i'm not. Do I just combine? Coz what I did was multiplied within the parentheses.

Answer 15

First, you evaluate
\[\Large [3x+10]^2\]

Answer 16

6x+20 right?

Answer 17

9x sorry

Answer 18

ugh wait 9x+100

Answer 19

@terenzreignz

Answer 20

Could you review the FOIL method or the method of squaring a binomial?

Or, as a quick reference, look at this...
\[\Large (\color{red}a+\color{blue}b)^2 = \color{red}a^2 + 2\color{red}a\color{blue}b+\color{blue}b^2\]

Answer 21

By that logic, what is
\[\Large (\color{red}{3x}+ \color{blue}{10})^2= \qquad?\]

Answer 22

ahhh okay 3^2+2(3)(10)+10^2 like that?

Answer 23

Do remember the x...
your 'a' in this case is not simply 3 but 3x

Answer 24

okay 3x^2+2(3x)(10)+10^2

Answer 25

then combine?

Answer 26

\[\large3x^2\qquad \color{red}?\]

Answer 27

I don't understand what you're asking

Answer 28

Why is it 3x^2 ?
What is the square of 3x ?

Answer 29

oh 9x^2

Answer 30

better. Okay, so simplify?

Answer 31

okay 3x^2+2(3x)(10)+10^2= 9x+6x+5+100

Answer 32

or I mean 105?

Answer 33

Why do you have 3x^2 again? -.-

Answer 34

no I changed it to 9x+6x+105

Answer 35

let's start again...
\[\Large (3x)^2+2(3x)(10)+10^2\]
And simplify this one at a time, please.

Answer 36

okay so (3x)^2=9x

Answer 37

9x^2 !!!

Answer 38

where are you getting 9x^2 from? but anyways 81x

Answer 39

No... I mean, you square both the 3 and the x -.-
\[\Large (3x)^2=\color{red}{9x^2}\]

Answer 40

oh okay. Got it

Answer 41

9x^2+6x+5+100x^2 better?

Answer 42

Nope. Now what about this part (in red)?
It's just multiplication.
\[\Large9x^2 + \color{red}{2(3x)(10)}+10^2\]

Answer 43

sorry 6x+20 right?

Answer 44

wrong.
what's 2(3x)(10)

Answer 45

60x

Answer 46

right. now this.
\[\Large 9x^2 + 60x +\color{red}{10^2}\]

Answer 47

100

Answer 48

\[\Large 9x^2 +60x + 100\]
And this is what we put in this place...
\[\Large f[g(x)]= 2 - \color{red}{[g(x)]^2}\]

Answer 49

omg sorry for taking up so much of your time

Answer 50

you won't be for longer, lol, I have to get to class in a few minutes

Answer 51

ah okay thanks anyways!

Answer 52

I'm sure there are other people on OS who can help you out, but unfortunately, for the moment, I have to go :D
--------------------------------------------
Terence out

Answer 53

Still need help with this problem?

Answer 54

yes!

Answer 55

the person answered a different question before this

Answer 56

this problem?
Given f(x) = 6x2 – x – 12 and g(x) = 2x – 3, find the function (fg)(x).

Evaluate the composite function f(g(x)) for x = 31.

Answer 57

before we start though, do you know what g(2) = ?

Answer 58

no they didn't answer that. and no..

Answer 59

g(2) is what you get when you plug 2 for x in g(x)

Answer 60

g(2) = 2(2) -3 = 1

Answer 61

since g(x) = 2x - 3

Answer 62

so f(g(x)) is the same principle. we plug in g(x) in every x in f(x), same way that g(2) is plugging 2 in every x of g(x)

Answer 63

so f(g(x)) = 6[g(x)]^2 - g(x) - 12

do you follow so far?

Answer 64

Ohh okay

Answer 65

so we have:

\[f(g(x)) = 6(2x - 3)^2 - (2x -3) -12\]

knowing the shortcut, by habit, that:

\[(a+b)^2 = a^2 + 2ab + b^2\] i'll save my self a small step and a small mess to expand.

\[f(g(x)) = 6(4x^2 - 12x + 9) - 2x + 3 - 12 = 24x^2 -74x + 45\]

that's (fg)(x). now they ways (fg)(31) which is equivalent to f(g(31)) [diffrent notation]

plug in 31 for every x in f(g(x))

Answer 66

now they want**

Answer 67

:/ oof this..problem looks intimidating

Answer 68

it's easier than it seems. and with a bit of practice they will become very easy and second nature.

i have may have complicated things with the "shortcut". expanding with foil is as good.

don't let math intimidate you, it's your friend :)

and we're here to help you love it!

Answer 69

okay so with every x in there I replace is with a 31? @Euler271

Answer 70

yup

Answer 71

okay 6(4(31)^2-12(31)+9)-2(31)+3-12=24(31)^2+74(31)+45

Answer 72

@Euler271

Answer 73

ya they would be the same thing

Answer 74

Um for the first part I get 20815... @Euler271

Answer 75

i get 25403

Answer 76

oh okay the 2nd part I get 25403 too

Answer 77

@Euler271

Answer 78

cool ^_^

thats the final answer

Answer 79

Oh! @euler. those were both two different problems though...

Answer 80

@euler this was for the 2nd problem