# compose

Functional composition

## Syntax

``compose(f,g)``
``compose(f,g,z)``
``compose(f,g,x,z)``
``compose(f,g,x,y,z)``

## Description

example

````compose(f,g)` returns `f(g(y))` where `f = f(x)` and ```g = g(y)```. Here `x` is the symbolic variable of `f` as defined by `symvar` and `y` is the symbolic variable of `g` as defined by `symvar`.```

example

````compose(f,g,z)` returns `f(g(z))` where `f = f(x)`, ```g = g(y)```, and `x` and `y` are the symbolic variables of `f` and `g` as defined by `symvar`.```

example

````compose(f,g,x,z)` returns `f(g(z))` and makes `x` the independent variable for `f`. That is, if `f = cos(x/t)`, then `compose(f,g,x,z)` returns `cos(g(z)/t)` whereas `compose(f,g,t,z)` returns `cos(x/g(z))`.```

example

````compose(f,g,x,y,z)` returns `f(g(z))` and makes `x` the independent variable for `f` and `y` the independent variable for `g`. For `f = cos(x/t)` and ```g = sin(y/u)```, `compose(f,g,x,y,z)` returns `cos(sin(z/u)/t)` whereas `compose(f,g,x,u,z)` returns `cos(sin(y/z)/t)`.```

## Examples

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Show functional composition by creating functions from existing functions.

Declare functions.

```syms x y z t u f = 1/(1 + x^2); g = sin(y); h = x^t; p = exp(-y/u);```

Compose functions with different functions and variables as inputs.

`a = compose(f,g)`
```a = 1/(sin(y)^2 + 1)```
`b = compose(f,g,t)`
```b = 1/(sin(t)^2 + 1)```
`c = compose(h,g,x,z)`
```c = sin(z)^t```
`d = compose(h,g,t,z)`
```d = x^sin(z)```
`e = compose(h,p,x,y,z)`
```e = exp(-z/u)^t ```

## Input Arguments

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Input, specified as a symbolic function or expression.

Input, specified as a symbolic function or expression.

Symbolic variable, specified as a symbolic variable.

Symbolic variable, specified as a symbolic variable.

Symbolic variable, specified as a symbolic variable.