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

- anonymous

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

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- schrodinger

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- anonymous

@shivamgautam can you help with this as well?

- anonymous

u mean we have to find f(x) right?

- anonymous

@WaVVessux

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## More answers

- anonymous

(fg)(x)

- anonymous

if that is right then
first of all find x from g(x)=2x-3
as x=3/2
now put value of x in f(x):
6(3/2)^2 - 3/2 - 12

- anonymous

okay is that the answer?

- anonymous

k its easy (fg)(x) means f(x)*g(x)

- anonymous

alright, so now I solve then?

- anonymous

now continue with above process
f(x) = 6.9/4 - 3/2 -12
= 54/4 - 3/2 -12
= 27/2 - 3/2 -12
= 24/ 2 - 12 = 0

- anonymous

Oh okay I got 0 but I didn't think it was right

- anonymous

what is the answer?

- anonymous

...I'm lost :/

- anonymous

wait a min i will get back to shortly

- anonymous

Okay

- anonymous

k here we have to find (fg)(x) it means (fx)*(gx)

- anonymous

so first multiple both functions

- anonymous

we will get 12 x^3-20 x^2-21 x+36

- anonymous

now we can solve this using cube formula

- anonymous

should i give u all steps!

- Jhannybean

Allyou have to do is multiply these two functions.. :)
Omg the cube formula.. -_-

- anonymous

and answer will be 3/2 and -4/3

- anonymous

but, I need it in polynomial standard form...

- anonymous

k

- anonymous

we can use alternate forms to solve this
12 x^3-20 x^2-21 x+36
alternative form is
(3-2x)^2(3x+4)

- anonymous

now we can solve them separately as 3x+4=0
9+4x^2-12x

- anonymous

And that's it? :D

- anonymous

(1) 3x+4=0
3x=-4
x=-4/3
(2) 4x^2-12x+9=0
so after solving it from quadratic formula:
x=3/2

- anonymous

and that it!!! :)

- anonymous

For the standard polynomial form?

- anonymous

and we could have solved it from the first answer i told u by find x from 3/2
after putting value of x in f(x) we get zero that means 3/2 satisfies the f(x) therefore 3/2 is the answer!! :)

- anonymous

##### 1 Attachment

- anonymous

@McLove

- anonymous

12 x^3-20 x^2-21 x+36 (this will be the answer for standard polynomial form)

- anonymous

Much gratitude.

- Jhannybean

Hm..

- anonymous

??

- anonymous

@Jhannybean
first take look at the question we were given
it is f(x)=6x2 – x – 12
and
g(x) = 2x-3

- Jhannybean

f x g = (6x^2 - x - 12)(2x - 3) =
12x^3 - 2x^2 -24x -18x^2 +3x+36
12x^3 -20x^2 -21x +36

- anonymous

first alternative can be found by above info
so just simply f(x) and ur alternative form will be there

- anonymous

did u get it @Jhannybean

- Jhannybean

Hm... first alternative? let me scroll up and see...

- anonymous

oh sorry i mean alternative

- Jhannybean

Yeah... that's where im getting stuck.
"alternative form is
(3-2x)^2(3x+4)"
how did you derive this equation to standard form?

- Jhannybean

I mean....break it down into those....

- anonymous

we first break f(x) and will get (2x-3)(4+3x)

- anonymous

now as we have g(x) to answer will be
12 x^3-20 x^2-21 x+36 = (2x-3)(4+3x)(2x-3)

- Jhannybean

ohhhh!!! HAHA got it.

- anonymous

as we have two 2x-3 it will be (2x-3)^2(4+3x)

- Jhannybean

SMART. i don't know why i didnt see that.... lol.

- anonymous

hehe :) u forgot g(x)

- Jhannybean

yep.

- anonymous

bye

- Jhannybean

i was trying to work back from the expanded form and i was like.... what!?

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