Question

I always had trouble doing these..Can someone clearly explain on how to do these type of problems starting with this question: f(x)= 4x/(1-x) and g(x)= 2/x, then f(g(x))=?

Answer 1

ok. I'll try

Answer 2

work from the middle of the f(g(x))
g(x)=2/x
so everytime you see a g(x), plug in 2/x, because they're the same thing.

Answer 3

like this f((2/x)) ??

Answer 4

\[f(g(x))=f\left(\frac{2}{x}\right)\]

yes

Answer 5

Now, help me out Zarkon if I'm wrong here, but I believe u plug in the f(x)equation and put 2 over it

Answer 6

every where you see an x in the function f(x) replace it with 2/x

Answer 7

I think that Zarkon might be right. I was just guessing for mine.

Answer 8

I am ;)

Answer 9

Okay so I did that Zarkon, we know have 4(2x)/1-2x and also the 2/x

Answer 10

try again

Answer 11

you replaced x with 2x not 2/x

Answer 12

\[4(2/x)\div \left( 1-(2/x) \right)\]

Answer 13

yes

Answer 14

$$f(x)=\frac{4x}{1-x}$$

$$f\left(\frac{2}{x}\right)=\frac{4\left(\frac{2}{x}\right)}{1-\left(\frac{2}{x}\right)}$$

Answer 15

Opps sorry, I corrected it now...so how do we solve that

Answer 16

that is it

Answer 17

you can simplify if you like

Answer 18

cancel out the (2/x)

Answer 19

multiply top and bottom by x

Answer 20

dat works too

Answer 21

then what would u have Sarah blu?

Answer 22

hmm I am getting the answer 8/-1 .. i am not sure i am understanding when you mean multiply top and bottom by x

Answer 23

$$\frac{4\left(\frac{2}{x}\right)}{1-\left(\frac{2}{x}\right)}\frac{x}{x}=\frac{8}{x-2}$$

Answer 24

understand?

Answer 25

why is the x still in the denominator?

Answer 26

\[\left(1-\frac{2}{x}\right)x=1\cdot x-\frac{2}{x}\cdot x=x-2\]

Answer 27

distribute

Answer 28

ok?

Answer 29

Ohhhhhh that makes soo much sense now..Thank you so much :) !! you too gandalfwiz

Answer 30

aww thanks!