Functional as a Multivariable Function

A functional dependent on a function is analogous to a multivariable function dependent on a vector of variables. For example, consider the functional 

To extend the analogy further, consider a functional dependent on an integral of a continuous function. The latter has an infinite number of components over a non-zero range of integration. Thus, the functional is equivalent to a multivariable function dependent on the variable vector comprising those components. For example, the functional I in Equation (2.1) is equivalent to a multivariable function dependent on a vector of infinite components of /. 

An interesting upshot of the above analogy is that a continuous function is equivalent to a vector of infinite components. Thus, /(x) in Equation (2.1) is equivalent to the vector 

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