# How do you prove algebraically (not graphically): f (x) =(2x-3)/(3x-2) is one to one function?

Dec 10, 2016

See explanation.

#### Explanation:

${f}^{- 1} \left(y\right) = x = \frac{2 y + 3}{3 y - 2}$. Readily, the asymptotes are $x = \frac{2}{3} = y$.

But for this end behavior, y is bijective.

I don't think that graph should not be included. What is said in

algebra is seen in a graph.

Have a look at the rectangular hyperbola that depicts this equation.

graph{y(3x-2)-2x+3=0 [-10, 10, -5, 5]}