Question

Given f(x) = 6x^2 - x - 12 and g(x) = 2x - 3, find the function (f/g)(x). Enter your answer as the following example: -10x+1.

Answer 1

what does the (f/g)(x) mean

Answer 2

this one you need to write a fraction first
\[\frac{6x^2-x-12}{2x-3}\]

Answer 3

so its dividing?

Answer 4

\[f/g\] means
\[\frac{f(x)}{g(x)}\] yes it is dividing

Answer 5

yeah i got that equation but i dont know what to do from there..

Answer 6

my guess is that you can actually divide, i.e. you can factor the numerator and cancel
lets check it

Answer 7

\[6x^2-x-12=(2x-3)(3x+4)\] so you get
\[\frac{6x^2-2x-12}{2x-3}=\frac{(2x-3)(3x+4)}{2x-3}=3x+4\]

Answer 8

the clue that you could factor and cancel came from this line here in your question
"Enter your answer as the following example: -10x+1."

Answer 9

oh, thanks again, lol i feel stupid.... :(

Answer 10

since they did not expect you to put in a fraction, it was clear that the numerator had to factor as \((2x-3)(\text{something})\) otherwise there would be nothing to do

Answer 11

don't feel stupid! this is just math, you learn it, you are not born with it

Answer 12

haha yeah, im in a lesson on my online school and i dont understand the way they teach so i have to look it all up online. :( thanks for helping, i understand it a bit better than when they taught me..

Answer 13

glad to help, keep posting
on line classes are difficult, because there is no one to ask if you have a question

Answer 14

wait so cactus high is on line?

Answer 15

i might have more questions soon though