anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Much gratitude to whoever helps me. I just can't get these. I hate alg 2
terenzreignz
  • terenzreignz
f + g ? You just add f(x) and g(x)
anonymous
  • anonymous
would the answer just be x^2? for that one?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

terenzreignz
  • terenzreignz
As a matter of fact, yes :D
terenzreignz
  • terenzreignz
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)
terenzreignz
  • terenzreignz
\[\large f(\color{orange}x) =2 - \color{orange}x^2\]\[\large \color{red}{g(x)=3x+10}\] \[\Large f[\color{red}{g(x)}]=2-[\color{red}{g(x)}]^2\]
anonymous
  • anonymous
And then I just solve that?^
terenzreignz
  • terenzreignz
replace g(x) and then solve from there, yes :D
anonymous
  • anonymous
okay I get x-5. Is that correct?
terenzreignz
  • terenzreignz
I don't think so. Remember \[\large g(x) = 3x+10\]
anonymous
  • anonymous
hmmm, is it 6x+20?
terenzreignz
  • terenzreignz
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... \[\Large f[\color{red}{g(x)}]=2-[\color{red}{3x+10}]^2\]
terenzreignz
  • terenzreignz
and carry on from there...
anonymous
  • anonymous
No i'm not. Do I just combine? Coz what I did was multiplied within the parentheses.
terenzreignz
  • terenzreignz
First, you evaluate \[\Large [3x+10]^2\]
anonymous
  • anonymous
6x+20 right?
anonymous
  • anonymous
9x sorry
anonymous
  • anonymous
ugh wait 9x+100
anonymous
  • anonymous
@terenzreignz
terenzreignz
  • terenzreignz
Could you review the FOIL method or the method of squaring a binomial? Or, as a quick reference, look at this... \[\Large (\color{red}a+\color{blue}b)^2 = \color{red}a^2 + 2\color{red}a\color{blue}b+\color{blue}b^2\]
terenzreignz
  • terenzreignz
By that logic, what is \[\Large (\color{red}{3x}+ \color{blue}{10})^2= \qquad?\]
anonymous
  • anonymous
ahhh okay 3^2+2(3)(10)+10^2 like that?
terenzreignz
  • terenzreignz
Do remember the x... your 'a' in this case is not simply 3 but 3x
anonymous
  • anonymous
okay 3x^2+2(3x)(10)+10^2
anonymous
  • anonymous
then combine?
terenzreignz
  • terenzreignz
\[\large3x^2\qquad \color{red}?\]
anonymous
  • anonymous
I don't understand what you're asking
terenzreignz
  • terenzreignz
Why is it 3x^2 ? What is the square of 3x ?
anonymous
  • anonymous
oh 9x^2
terenzreignz
  • terenzreignz
better. Okay, so simplify?
anonymous
  • anonymous
okay 3x^2+2(3x)(10)+10^2= 9x+6x+5+100
anonymous
  • anonymous
or I mean 105?
terenzreignz
  • terenzreignz
Why do you have 3x^2 again? -.-
anonymous
  • anonymous
no I changed it to 9x+6x+105
terenzreignz
  • terenzreignz
let's start again... \[\Large (3x)^2+2(3x)(10)+10^2\] And simplify this one at a time, please.
anonymous
  • anonymous
okay so (3x)^2=9x
terenzreignz
  • terenzreignz
9x^2 !!!
anonymous
  • anonymous
where are you getting 9x^2 from? but anyways 81x
terenzreignz
  • terenzreignz
No... I mean, you square both the 3 and the x -.- \[\Large (3x)^2=\color{red}{9x^2}\]
anonymous
  • anonymous
oh okay. Got it
anonymous
  • anonymous
9x^2+6x+5+100x^2 better?
terenzreignz
  • terenzreignz
Nope. Now what about this part (in red)? It's just multiplication. \[\Large9x^2 + \color{red}{2(3x)(10)}+10^2\]
anonymous
  • anonymous
sorry 6x+20 right?
terenzreignz
  • terenzreignz
wrong. what's 2(3x)(10)
anonymous
  • anonymous
60x
terenzreignz
  • terenzreignz
right. now this. \[\Large 9x^2 + 60x +\color{red}{10^2}\]
anonymous
  • anonymous
100
terenzreignz
  • terenzreignz
\[\Large 9x^2 +60x + 100\] And this is what we put in this place... \[\Large f[g(x)]= 2 - \color{red}{[g(x)]^2}\]
anonymous
  • anonymous
omg sorry for taking up so much of your time
terenzreignz
  • terenzreignz
you won't be for longer, lol, I have to get to class in a few minutes
anonymous
  • anonymous
ah okay thanks anyways!
terenzreignz
  • terenzreignz
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
anonymous
  • anonymous
Still need help with this problem?
anonymous
  • anonymous
yes!
anonymous
  • anonymous
the person answered a different question before this
anonymous
  • anonymous
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.
anonymous
  • anonymous
before we start though, do you know what g(2) = ?
anonymous
  • anonymous
no they didn't answer that. and no..
anonymous
  • anonymous
g(2) is what you get when you plug 2 for x in g(x)
anonymous
  • anonymous
g(2) = 2(2) -3 = 1
anonymous
  • anonymous
since g(x) = 2x - 3
anonymous
  • anonymous
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)
anonymous
  • anonymous
so f(g(x)) = 6[g(x)]^2 - g(x) - 12 do you follow so far?
anonymous
  • anonymous
Ohh okay
anonymous
  • anonymous
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))
anonymous
  • anonymous
now they want**
anonymous
  • anonymous
:/ oof this..problem looks intimidating
anonymous
  • anonymous
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!
anonymous
  • anonymous
okay so with every x in there I replace is with a 31? @Euler271
anonymous
  • anonymous
yup
anonymous
  • anonymous
okay 6(4(31)^2-12(31)+9)-2(31)+3-12=24(31)^2+74(31)+45
anonymous
  • anonymous
@Euler271
anonymous
  • anonymous
ya they would be the same thing
anonymous
  • anonymous
Um for the first part I get 20815... @Euler271
anonymous
  • anonymous
i get 25403
anonymous
  • anonymous
oh okay the 2nd part I get 25403 too
anonymous
  • anonymous
@Euler271
anonymous
  • anonymous
cool ^_^ thats the final answer
anonymous
  • anonymous
Oh! @euler. those were both two different problems though...
anonymous
  • anonymous
@euler this was for the 2nd problem
1 Attachment

Looking for something else?

Not the answer you are looking for? Search for more explanations.