Question

let f(x)=x/(x-2) . find a function y=g(x) so that
(f°g)(x)=3x
g(x)= ?? anybody can help??

Answer 1

there is a catch here, x can't be 3. but otherwise the solution is easy

Answer 2

actually i don't understand the whole thing

Answer 3

let \[g(x) = y\]
so, \[f(g(x)) = 3x \Rightarrow f(y) = 3x \Rightarrow \frac{y}{y-2} = 3x\]
which gives
\[y = \frac{6x}{3x-1}\]
Hence
\[g(x) = \frac{6x}{3x -1 }\]
for a check, just plug in the f(g(x)) and see it equals 3x, but remember
\[x \neq \frac{1}{3}\]

Answer 4

yes, sure !! thank you