composite function

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compos′ite func′tion

n. Math.
a function obtained from two given functions, where the range of one function is contained in the domain of the second function, by assigning to an element in the domain of the first function that element in the range of the second function whose inverse image is the image of the element.
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The idea for constructing such composite function has occurred by observing property that accuracy in approximating the Q-function depends on the fitting parameters, which further strictly, depend on the range of argument.
The blocks of the 2nd and following hidden layers produce extended neurons composite terms (CT), which substitute for the composite function derivatives in respect of the output and input variables of the back connected previous layer blocks, e.g.
For the case where composite function has several intermediate variables, set z = f[u, v, [omega]], u = [phi](t), v = [psi](t), and [omega] = [omega](t) and then get the composite function z = f[[phi](t),[psi](t),[omega](t)].
Huang, "Composite function wavelet neural networks with differential evolution and extreme learning machine," Neural Processing Letters, vol.
Let [PHI]([[xi].sub.1](t), [[xi].sub.2](t), ..., [[xi].sub.r](t)) be a composite function for which delta derivatives up to order a + b, where a and b are nonnegative integers, are defined.
Bergweiler, "On the Nevanlinna characteristic of a composite function," Complex Variables, vol.
(1) For the composite function of the function f(x), [PI][f(x)], its reconstruction (or approximation) formula is
The determinant of the Hessian matrix of a composite function f = F([h.sub.1]([x.sub.1]) + ...
Express f([g.sub.1](x,y), [g.sub.2](x,y))in terms of x and y, and find the domain of the resulting composite function. Substituting [g.sub.1](x,y) for x, [g.sub.2](x,y) for y, in the expression for f(x,y)then f([g.sub.1](x,y), [g.sub.2](x,y)) = [([x.sup.2] + [y.sup.2]).sup.x-y], the domain is [E.sub.2] = R x R- {[0,0]}.
The derivative of a composite function, taken with the chain rule is one of the important notions in calculus.
[13] Wu Qibin, A composite function involving the Smarandache function, Pure and Applied Mathematics, Vol.
This paper discusses the responses of 20 prospective elementary and special education mathematics specialists to questions about conceptualization of the function concept as well as facility with composite functions. Results indicate that many of the prospective teachers held historical definitions tied to formulaic rules and that this negatively affected their ability to solve composite function problems.