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Creates a new function that is the composition of two other functions.

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`

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}
```

Updated by **Greiser**, **8 weeks ago **– be80871