inverse function

[spacewater]

problem
\(\displaystyle f(x) = \frac {3x}{x-5}\)
steps
\(\displaystyle y = \frac{3x}{x-5}\)

\(\displaystyle x = \frac {3y}{y-5}\)

\(\displaystyle x(y+5)=\frac{3y}{y-5}\cdot\frac{y+5}{y+5}\)

\(\displaystyle xy + 5x = \frac {3y}{y+5}\)

well this is where my endeavor ends... been a confusing trip but without any solution... care for help? the final coming up next week.. :roll:

 

[Aladdin]

\(\displaystyle 3x=xy-5y\)

\(\displaystyle 3x-xy=-5y\)

\(\displaystyle x(3-y)=-5y\)

\(\displaystyle x=\frac{-5y}{3-y}\)

\(\displaystyle y=\frac{-5x}{3-x}\)

 

[Loren]

problem
\(\displaystyle f(x) = \frac {3x}{x-5}\)
steps
\(\displaystyle y = \frac{3x}{x-5}\)

\(\displaystyle x = \frac {3y}{y-5}\)

\(\displaystyle x(y+5)=\frac{3y}{y-5}\cdot\frac{y+5}{y+5}\) <<<should be \(\displaystyle x(y-5)=3y\)
then xy-5x=3y
xy-3y=5x
y(x-3) = 5x
\(\displaystyle y=\frac{5x}{x-3}\) Done?

\(\displaystyle xy + 5x = \frac {3y}{y+5}\)

well this is where my endeavor ends... been a confusing trip but without any solution... care for help? the final coming up next week.. :roll: