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As indicated earlier, the ln(x) and exp(x) functions are inverse of each other,
i.e., ln(exp(x)) = x, and exp(ln(x)) = x. This can be verified in the calculator by
typing and evaluating the following expressions in the Equation Writer:
LN(EXP(X)) and EXP(LN(X)). They should both evaluate to X.
When a function f(x) and its inverse f
-1
(x) are plotted simultaneously in the
same set of axes, their graphs are reflections of each other about the line y = x.
Let’s check this fact with the calculator for the functions LN(X) and EXP(X) by
following this procedure:
Press, simultaneously if in RPN mode, „ñ. The function Y1(X) = EXP(X)
should be available in the PLOT - FUNCTION window from the previous
exercise. Press @@ADD@! , and type the function Y2(X) = LN(X). Also, load
the function Y3(X) = X. Press L@@@OK@@@ to return to normal calculator display.
Press, simultaneously if in RPN mode, „ò, and change the H-View range
to read: H-View: -8 8
Press @AUTO to generate the vertical range. Press @ERASE @DRAW to produce the
graph of y = ln(x), y = exp(x), and y =x, simultaneously if in RPN mode.
You will notice that only the graph of y = exp(x) is clearly visible. Something
went wrong with the @AUTO selection of the vertical range. What happens is that,
when you press @AUTO in the PLOT FUNCTION – WINDOW screen, the
calculator produces the vertical range corresponding to the first function in the
list of functions to be plotted. Which, in this case, happens to be Y1(X) =
EXP(X). We will have to enter the vertical range ourselves in order to display
the other two functions in the same plot.
Press @CANCL to return to the PLOT FUNCTION – WINDOW screen. Modify the
vertical and horizontal ranges to read: H-View: -8 8, V-View: -4 4
By selecting these ranges we ensure that the scale of the graph is kept 1 vertical
to 1 horizontal. Press @ERASE @DRAW and you will get the plots of the natural
logarithm, exponential, and y = x functions. It will be evident from the graph
that LN(X) and EXP(X) are reflections of each other about the line y = X. Press
@CANCL to return to the PLOT WINDOW – FUNCTION. Press ` to return to
normal calculator display.