Inverse Functions:

Purpose:  To graph a function, f(x), on the same set of axes as it’s inverse, f -1 (x), to observe the symmetry in the graphs of f(x) and f -1 (x), and to then verify the two functions are inverses by locating corresponding points on the table.    

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We will examine the function .

We first want to find it’s inverse function.  A function’s inverse is the new function created by simply interchanging the domain and the range values.

So, let’s interchange the x and y values.

Now, solve for y and rename the function f inverse.

Now let’s go to:

Main MENU and

select 5, Graph.

Enter:

Y1 as 2x+6

Y2 as (x – 6) / 2

Y3 as x

Then press the Blue EXE Key on the calculator key pad.

Press SHIFT and V-Window

Select the F3 (or) STD window.

This sets your standard viewing window on a domain of [-10, 10]

and a range of [-10, 10]

it is helpful to have a square window to observe the symmetry.

Press SHIFT and Quit

Select the F6 (or) DRAW.

The graph of the three functions

should appear.

Observe the symmetry about

the line y = x.

Return to the Main MENU

Select 7, TABLE

Then Press TABL

Observe the point (1, 8).

Go to the second row and

change the 2 in the x column to 8.

You will see the Y2 column display a 1.

So, (1,8) on f corresponds to (8,1) to f -1.

Handout author: Jay Abramson

last update: 11/21/01 sw