Inverse functions

 

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

Interchange x and y in the given expression.

\[ \begin{align} x &= \sqrt y \\ \end{align} \ \]

Solve for y.

\[ \begin{align} x &= \sqrt y \\ x^2 &= (\sqrt y)^2 \\ y &= x^2 \\ \end{align} \ \]

Sketch the graph.

Your sketch should be similar to the figure below.

  

Important This is not a 'textbook on a screen' - this is an interactive learning system. Which means you have to 'act' to make it go.

Look through the options below and select the one you think is the best response. You will gain most benefit if you work the problem with pen and paper as you go, i.e. decide what you think is the correct option and write down what you think the result will be before you click. If the next step doesn't display, click another option.

 

The first step in finding an inverse function is?

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Now You Try:

Find the inverse function of \[ \begin{align} y &= x^2 + 1 \\ \end{align}\ \] for x > 0, and sketch its graph.

 

Invert the right hand side of the expression.
Solve for x.
Interchange x and y in the given expression.