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@shivamgautam can you help with this as well?
u mean we have to find f(x) right?
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
okay is that the answer?
k its easy (fg)(x) means f(x)*g(x)
alright, so now I solve then?
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
Oh okay I got 0 but I didn't think it was right
what is the answer?
...I'm lost :/
wait a min i will get back to shortly
k here we have to find (fg)(x) it means (fx)*(gx)
so first multiple both functions
we will get 12 x^3-20 x^2-21 x+36
now we can solve this using cube formula
should i give u all steps!
Allyou have to do is multiply these two functions.. :) Omg the cube formula.. -_-
and answer will be 3/2 and -4/3
but, I need it in polynomial standard form...
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)
now we can solve them separately as 3x+4=0 9+4x^2-12x
And that's it? :D
(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
and that it!!! :)
For the standard polynomial form?
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!! :)
12 x^3-20 x^2-21 x+36 (this will be the answer for standard polynomial form)
@Jhannybean first take look at the question we were given it is f(x)=6x2 – x – 12 and g(x) = 2x-3
f x g = (6x^2 - x - 12)(2x - 3) = 12x^3 - 2x^2 -24x -18x^2 +3x+36 12x^3 -20x^2 -21x +36
first alternative can be found by above info so just simply f(x) and ur alternative form will be there
did u get it @Jhannybean
Hm... first alternative? let me scroll up and see...
oh sorry i mean alternative
Yeah... that's where im getting stuck. "alternative form is (3-2x)^2(3x+4)" how did you derive this equation to standard form?
I mean....break it down into those....
we first break f(x) and will get (2x-3)(4+3x)
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)
ohhhh!!! HAHA got it.
as we have two 2x-3 it will be (2x-3)^2(4+3x)
SMART. i don't know why i didnt see that.... lol.
hehe :) u forgot g(x)
i was trying to work back from the expanded form and i was like.... what!?