f(g(x)) equation: f(x) = 4x over 1 - x, g(x) = 2 over x

[davinea]

i have been having so much trouble figuring out how this problem is supposed to be solved. can someone help me understand this?

f(x)=4x over 1-x

g(x)=2 over x

( i don't know how to make fractions on the computer yet, so sorry if this is confusing)

how do you solve f(g(x))??

 

[soroban]

Re: someone help! f(g(x)) equation

Hello, davinea!

\(\displaystyle \text{Given: }\:\begin{array}{ccc}f(x)&=&\frac{4x}{1-x} \\ \\[-3mm] g(x)&=&\frac{2}{x} \end{aray}\)

\(\displaystyle \text{Find: }\:f(g(x))\)

\(\displaystyle \text{We have: }\;f(g(x)) \;=\;f\left(\frac{2}{x}\right) \;=\;\frac{4\left(\frac{2}{x}\right)}{1 - \frac{2}{x}}\)

\(\displaystyle \text{Multiply by }\frac{x}{x}\!:\quad\frac{x\;\left(\frac{8}{x}\right)} {x\left(1 - \frac{2}{x}\right)} \;=\; \frac{8}{x-2}\)

 

[davinea]

Re: someone help! f(g(x)) equation

thank you soo much. that has been bothering me all day. i have never been very good at math. thank you again for your help.