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# compose

Functional composition

## Syntax

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

## Description

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.

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.

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)).

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

Suppose

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

Then

```a = compose(f,g)
b = compose(f,g,t)
c = compose(h,g,x,z)
d = compose(h,g,t,z)
e = compose(h,p,x,y,z)
f = compose(h,p,t,u,z)```

returns:

```a =
1/(sin(y)^2 + 1)

b =
1/(sin(t)^2 + 1)

c =
sin(z)^t

d =
x^sin(z)

e =
exp(-z/u)^t

f =
x^exp(-y/z)```