Index

Working with MUMIE as author

Working with MUMIE as teacher

Using MUMIE via plugin in local LMS

FAQ for examination lecturers

Overview

Go back to the old wiki

We revise and update this wiki. We apologize for the inconvenience this may cause you.

# Substitute

Creates a new function by replacing a free variable by an earlier defined variable.
Main purposes are to obtain the composition of two functions or to evaluate a function at a given value.

1\substitute[<action>]{<variable>}{<expression>}{<free_variable>}{<substitute>} 
• action, variable and expression are identical to the input of a \function command.
• free_variable defines the free variable in the given expression.
• substitute must be an earlier defined variable. The free_variable will be replaced with the substitute variable.
• $$h = f \circ g$$ is the output of
1\substitute{h}{f}{x}{g} 
• This command can also be used to determine the value of a given function at a specific point $$x_0$$ (using a constant function variable). For example, $$6^4 - 5 \cdot 6^3 + 4 \cdot 6^2 + 3 \cdot 6 + 7$$ could be the output of
123\function{f}{x^4 - 5x^3 + 4x^2 + 3x + 7}    % defines a function named f\randint{x0}{2}{9}                          % point where f is to be evaluated\substitute{fx0}{f}{x}{x0}                  % this is the function f at point x_0 
Be aware that you cannot directly substitute x by a literal number e.g. 2, but that you need a variable taking this value, e.g. by using \number{two}{2} and \substitute{f2}{f}{x}{two}.
You can also normalize, expand, sort and calculate the \derivative and \substitute command. They take the same option *action* as a normal \function. In fact, you would often want to normalize a derivative, compare the following output with the earlier example shown for derivative. $$f_1 = 4x^3 + 6x^2$$ is the output of  \derivative[normalize]{f_1}{x^4 + 2*x^3}{x}