Inverse functions

 

Find the inverse function of \[ \begin{align} y &= \frac{1}{x-1} \quad \end{align}\ \] for x > 0, y > 0 and sketch its graph.

Interchange x and y in the given expression.

\[ \begin{align} x &= \frac{1}{y-1} \end{align} \ \]

Solve for y.

\[ \begin{align} x(y-1) &= 1 \\ y-1 &= \frac{1}{x} \\ y &= \frac{1}{x} + 1 \\ \end{align} \ \]

Sketch the graph.

Your sketch should be similar to the figure below.

  

You will gain most benefit if you work through each problem first and then come back and check your work against the solution.

 

y

Now You Try:

Find the inverse function of \[ \begin{align} y &= 4 - 2x \quad \end{align}\ \] and sketch its graph.