Question

Given h(x) = 3x/-x-1 find h^-1(x)

Answer 1

ok that was wrong
solve
\[x=\frac{3y}{-y-1}\] for \(y\)

Answer 2

Multiply by -y-1?

Answer 3

\(\large\tt \begin{align} \color{black}{h(x) = \dfrac{3x}{-x-1}\\~\\
y=\dfrac{3x}{-x-1}\\~\\
-y=\dfrac{3x}{x+1}\\~\\
-yx-y=3x\\~\\
-y=3x+yx\\~\\
-y=x(3+y)\\~\\
x=\dfrac{-y}{y+3}\\~\\
\text{swap x and y}\\~\\
y=\dfrac{-x}{x+3}\\~\\
\color{red}{h^{-1}(x)=\dfrac{-x}{x+3}}\\~\\
}\end{align}\)