As a domain expert in mathematics, particularly in the field of calculus and mathematical analysis, I can explain the concept of the substitution of functions.

The substitution of functions, also known as function composition, is a way to combine functions to create new ones. It involves applying one function to the result of another function. If you have two functions, say \( f(x) \) and \( g(x) \), the composition of \( f \) with \( g \), denoted as \( f(g(x)) \) or \( f ∘ g(x) \), is a new function that takes an input \( x \), feeds it through \( g \) to get an intermediate result, and then feeds that intermediate result into \( f \) to get the final output.

For example, if \( f(x) = x^2 \) and \( g(x) = x + 3 \), then the composition \( f(g(x)) \) would be \( f(g(x)) = f(x + 3) = (x + 3)^2 \).

Substitution of functions is a fundamental concept in mathematics, allowing for the simplification of complex expressions and the exploration of the relationships between different functions.

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Brain damage can produce horrific effects, including paralysis, sensory loss, memory loss, and personality deterioration. ... The damaged brain has three methods of repair: Collateral sprouting. The axons of some healthy neurons adjacent to damaged cells may grow new branches. Substitution of function.read more >>