__How to use the calculator__

1 - Press the button "click here to start" to start the calculator (applet).

2 - Enter a formula for function f (x^2 for example) and press "enter". Two graphs are displayed: the graph of function f (in blue) that you input, a parabola, and the graph (in red) of the reversed ordered pairs.

__Interactive Tutorial__

1 - Enter sqrt(x) in the editing window of the calculator, which means f(x) = sqrt(x), and press enter. sqrt stands for square root. Is the graph of the reversed pairs (in red) that of a function? If it is the graph of a function, it is the inverse function of f(x) = sqrt(x). Find, analytically, the inverse function of f(x) = sqrt(x) and compare it to the graph obtained.

2 - Enter x^2 in the editing window, which means f(x) = x^2, and press enter. Is the graph of of the reversed pairs (in red) that of a function? If it is not a function, is f a one to one function?

3 - Enter x^3 in the editing window, which means f(x) = x^3, and press enter. Is the graph of of the reversed pairs (in red) that of a function? If it is, it has to be the graph of the inverse of f. Find a formula for the graph of the inverse of f.

Exercies: Use the graphing calculator above (applet) to determine which of theses functions have inverses and which do not have inverses.

1 - f(x) = x^4

2 - f(x) = sin(x)

3 - f(x) = ln(x)

4 - f(x) = exp(x)

5 - f(x) = 5

6 - f(x) = arcsin(x)

Solutions to above exercies

1 - f(x) = x^4 has no inverse, it is not a one to one.

2 - f(x) = sin(x) has no inverse, it is not a one to one.

3 - f(x) = ln(x) has an inverse: exp(x)

4 - f(x) = exp(x) has an inverse: ln(x)

5 - f(x) = 5 has no inverse, it is not a one to one.

6 - f(x) = arcsin(x) has an inverse: sin(x) with restricted domain -pi/2 > x > pi/2

More references on inverse functions and graphing calculators.

Inverse Function Definition.

More Graphing Calculators.