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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 =
(1/exp(z/u))^t
 
f =
x^(1/exp(y/z))

See Also

finverse, subs, syms

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