Question

f(x) = 6x2 - x - 12 and g(x) = 2x - 3 find the function (f/g)(x)

Answer 1

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

If your question is just asking to find the function \[\frac{f(x)}{g(x)}\]
then we just

place the f(x) here
------------------
place the g(x) here

the notation I'm using is the same as (f/g)(x)

Answer 2

But I can't simplify 6x^2 - x -12. So there is no real answer for this equation?

Answer 3

we could try to simplify 6^x-x-12 using b^2-4ac which is the discriminant.

Answer 4

(-1)^2-4(6)(-12) for a = 6, b = -1, and c = -12

Answer 5

if we have a perfect square number like 25 16 9 then we can factor
if we have a non-perfect square number like 3 -32... then we can't factor and have to use the quadratic equation (or just leave the problem alone in this case)

Answer 6

so from the discriminant
(-1)^2-4(6)(-12) = 1-24(-12) =1+288 =289 we have a perfect square .. because the square root of 289 is 17

Answer 7

so we can factor 6x^2-x-12... it becomes (2x-3)(3x+4)

Answer 8

Oh okay. so then the 2x -3 crosses each other out which leaves 3x+4?

Answer 9

yes! that's right! the 2x-3 terms cancels out

Answer 10

\[\frac{(2x-3)(3x+4)}{2x-3} \rightarrow 3x+4 \]

Answer 11

Okay so if the question is Given f(x) = x + 2 and g(x) = x2 - 4, find the function (fg)(x) then the answer would be x^3 -2x^2- 4x - 8

Answer 12

Or did I do that wrong? Sorry. Still trying to get the hang of this

Answer 13

so (fg(x) or f(x)(g(x)) means that we multiply the f(x) function with the g(x) function

Answer 14

f(x)(g(x) = \[(x+2)(x^2-4) \]
then we use foil method

Answer 15

\[x^3-4x+2x^2-8\]

Answer 16

you've done it right....it's just that my terms have been rearranged. It means the same thing

Answer 17

Okay got it! Thank you so much