Question

Ive been on this for 4 hours... F(x)= x/x-3. f(g(x))=2x. What does G(x) and how do you find it?

Answer 1

now you werent given g(x) right?

Answer 2

Nope. We need to find the G(x). Given the F(x) and f(g(x).

Answer 3

Just to be sure... G'(x) = g(x), right?
I mean, are you using G as a primitive of g?

Answer 4

capital G?
or lower case?

Answer 5

math is case sensitive

Answer 6

sorry. lowcase g

Answer 7

\[f(g(x))=\frac{g(x)}{g(x)-3}=2x\]
solve this for g:
\[\frac{g}{g-3}=2x\]

Answer 8

in that case its function composition

Answer 9

G(x) = (-6x) / (1-2x)

Answer 10

\[g=2x(g-3) =>g=2xg-6x=> \]
\[g-2xg=-6x=>g(1-2x)=-6x=>g=\frac{-6x}{1-2x} \]

Answer 11

okay, well you were given F(x) equals x/x-3 which means that
F(g(x))=g(x)/g(x)-3=2x
=g(x)=2x(g(x)-3)
=g(x)=2x(g(x))-6x
=g(x)-2x(g(x))=-6x
=g(x)(1-2x)=6x
=G(x)=-6x/1-2x

Answer 12

\[f(g(x)) = 2x\]
\[f(x) = \frac{x}{x-2} \implies f(g) = \frac{g}{g-2} \implies f(g(x)) = \frac{g(x)}{g(x) - 2} = 2x\]

So, we have:
\[g(x) = 2x(g(x) - 2)\]
\[g(x) - 2xg(x) = -4x\]
\[(1-2x)g(x) = -4x\]
\[g(x) = \frac{-4x}{1-2x}\]

Answer 13

Ops... I've made a mistake there. It should be x-3 on the denominator, not x-2. Sorry.

Answer 14

wow thank you. Took me forever but think I get it now