Inverse of a function
This applet shows the inverse relation of a function.
The inverse of is a relation . Graphically, the inverse relation is obtained by reflecting the graph of about the line .
Inverse of a function
Enter the rule for a function f(x) in the textbox at bottom-left. Click 'Show points' to display a point on the x-axis, and the point(s) corresponding to . Drag the blue point to change x.
What do you get as you drag x along the axis?
Click 'Show inverse' to display the entire inverse relation. Is it a function? You can click 'Vertical line test' to provide a vertical line which might help you decide.
Is It a Function?
Is the inverse of a function? Does it pass the Vertical Line Test?
Can You Make It a Function?
Can you change the domain of to make its inverse a function? Explain
Inverse of More Power Functions
Change to in the applet. You can either use the carrot key (shift + 6) or tap the keyboard icon in the input field to type in the function.
Is It a Function?
Is the inverse of a function? Does it pass the Vertical Line Test?
Inverse of (Still) More Power Functions
Change to in the applet. You can either use the carrot key (shift + 6) or tap the keyboard icon in the input field to type in the function
Is It a Function?
Is the inverse of a function? Does it pass the Vertical Line Test?
Can You Make It a Function?
Can you change the domain of to make its inverse a function? Explain
Try other power functions. Is there a way to tell whether a power function's inverse is itself a function? Either by looking at the equation or devising a fool-proof test? Exaplain.