Question

If
F(x) =2x/x-3
And
FoG(x) =5x


What is g(x)?

Answer 1

Fx x gx=5x
Gx=5x/fx

Answer 2

HI!!

Answer 3

that answer is kinda silly right?

Answer 4

\[f(g(x)) = \frac{2g(x)}{g(x) - 3} = 5x\]
solve for g(x)

Answer 5

\[2g(x) = 5x(g(x) - 3)\]
\[5x g(x) - 2 g(x) = 15x\]
\[g(x) (5x-2) = 15x\]
\[g(x) = \frac{15x}{5x-2}\]

Answer 6

that should work
i was going to suggest that \[F^{-1}\circ F(x)\circ G(x)=F^{-1}(5x)=G(x)\]

Answer 7

\[F(x)=\frac{2x}{x-3}\\
F^{-1}(x)=\frac{3x}{x-2}\]
\[F^{-1}(5x)=\frac{3\times 5x}{5x-2}\]