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compose(f,g)
compose(f,g,z)
compose(f,g,x,z)
compose(f,g,x,y,z)
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).
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 how symbolic computations can help you find analytical solutions to math and engineering problems.
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