Question

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

Answer 1

@shivamgautam can you help with this as well?

Answer 2

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

Answer 3

@WaVVessux

Answer 4

(fg)(x)

Answer 5

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

Answer 6

okay is that the answer?

Answer 7

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

Answer 8

alright, so now I solve then?

Answer 9

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

Answer 10

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

Answer 11

what is the answer?

Answer 12

...I'm lost :/

Answer 13

wait a min i will get back to shortly

Answer 14

Okay

Answer 15

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

Answer 16

so first multiple both functions

Answer 17

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

Answer 18

now we can solve this using cube formula

Answer 19

should i give u all steps!

Answer 20

Allyou have to do is multiply these two functions.. :)

Omg the cube formula.. -_-

Answer 21

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

Answer 22

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

Answer 23

k

Answer 24

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)

Answer 25

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

Answer 26

And that's it? :D

Answer 27

(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

Answer 28

and that it!!! :)

Answer 29

For the standard polynomial form?

Answer 30

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!! :)

Answer 31

@McLove

Answer 32

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

Answer 33

Much gratitude.

Answer 34

Hm..

Answer 35

??

Answer 36

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

Answer 37

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

12x^3 - 2x^2 -24x -18x^2 +3x+36

12x^3 -20x^2 -21x +36

Answer 38

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

Answer 39

did u get it @Jhannybean

Answer 40

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

Answer 41

oh sorry i mean alternative

Answer 42

Yeah... that's where im getting stuck.

"alternative form is
(3-2x)^2(3x+4)"

how did you derive this equation to standard form?

Answer 43

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

Answer 44

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

Answer 45

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)

Answer 46

ohhhh!!! HAHA got it.

Answer 47

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

Answer 48

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

Answer 49

hehe :) u forgot g(x)

Answer 50

yep.

Answer 51

bye

Answer 52

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