Question

Let f(x) = x/(x-6). Find a function y=g(x) so that (f o g)(x)=2x.

Answer 1

I've tried plugging in equations. I assume there is a systematic way to do it.

Answer 2

f^-1 (2x)

Answer 3

12x/(1-2x)

Answer 4

\[\frac{x}{x-6} = 2x\]
solve for 'x' and make that = g(x)

Answer 5

ok

Answer 6

maybe work lol

Answer 7

i dont think amistre

Answer 8

0 = 2x^2 -13x

0 = x(2x -13)

x = 0 or x = 13/2

Answer 9

its just a shot in the dark ;)

Answer 10

(fog)(x) = 2x
so taking f^-1(x) on both sides
g(x) = f^-1(2x)

Answer 11

so just find f^-1 and plug in 2x in place of x

Answer 12

yeah, but thats only if you wanna try it the easy way ... thats just not how I roll lol

Answer 13

him im getting -12x/(1-2x)

Answer 14

Are you confident on that? I am just confused at this point.

Answer 15

ill show you the work:

x/(x-6)=y
x=y(x-6)
x=yx-6y
x-yx=-6y
x(1-y)=-6y
x=-6y/(1-y)
f^-1(x)=-6x/(1-x)
f^1(2x)=-12x/(1-2x)

Answer 16

you can plug in and see if it works too I geuss

Answer 17

Oh thanks man. I should have known this. Sub the x's for the y's. Then plug it in. Thanks again.

Answer 18

no problem, i plugged it in and checked and I think it works