Prepared by: RAPHAEL V. PEREZ,
• In short, the reflector of the original
function at the radical axis y = x
• The original function is
and then the inverse function of f(x) is:
f-1(x) or F(x) in other books
• In terms of ordered pairs, the inverse of
f(x) = (a,b) is
f-1(x) = F(x) (b,a)
• In short, the inverse of the set:
f(x) = (a1,b1), (a2,b2), (a3,b3),…, (an+1,bn+1)
f-1 (x) = F(x) = (b1, a1), (b2,a2), (b3,a3),…,
Now, in terms of POLYNOMIAL FUNCTION. Here are
the steps to get the inverse function [f-1(x)] of the
original function f(x):
1. Change f(x) to “y” on the given function.
2. Invert the variables between x and y. The y variable
in (1) will be “x” and for x variable on right side will
3. Solve for y from (2).
4. Change “y” into f-1(x).
5. Solve for f [f-1(x)] and f-1[f(x)] (Composition Method).
The answer must be “x”.
POSSIBLE TO GRAPH ?
You may use the graphical software
for Cartesian and Polar coordinates
For graphing: you will graph only linear functions ( y = mx + b).
Other functions like:
exponential (y = bx)
logarithmic (y = logb x or y = ln x) ,
trigonometric (y = a sin x)
and second degree or higher polynomials
(y = axn + xn-1 +…+a0)
are not yet discussed for way of sketching the function, sometimes
you need to use programmable and graphical calculators or the
computers. It’s hard to sketch the mentioned functions.
If you want this application
program for graphing purposes
install on your Personal
this is a free-download software