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How to Handle Combinations & Composition of Functions

on the TI-89

As an example, define the functions f(x) = x2 - 4 and g(x) = sqrt(x).

f(x)=x^2-4, g(x)=sqrt(x)

Once 2 functions are defined, the calculator will combine them in any way you like, as shown at right. In fact, you can use f(x) or g(x) in any expression exactly as you would use a variable.

Note: The functions y1(x), y2(x), etc. defined on the "Y=" screen can be used in exactly the same way.

f(x) + g(x), etc.

Composition of functions can be handled in normal mathematical notation, as shown at right.

Warning: Although the TI-89 can be a very powerful tool for figuring out composition of functions, it doesn't handle domains. For instance, it is true that f(g(x)) = x - 4 in this example, but the domain of f(g(x)) is x >= 0 , not all real numbers as you might hastily assume by looking at "x - 4".

f(g(x)), etc.

last update August 30, 2009 by JL Stanbrough