When encountering the notation [tex]\(s(x)\)[/tex], it is crucial to understand that this denotes a function [tex]\(s\)[/tex] with [tex]\(x\)[/tex] as its input variable. The function [tex]\(s\)[/tex] maps the input [tex]\(x\)[/tex] to an output value, often written as [tex]\(s(x)\)[/tex].
Let's break down the given options:
A. This statement suggests that [tex]\(x\)[/tex] is a function of [tex]\(s\)[/tex], meaning [tex]\(x\)[/tex] would depend on [tex]\(s(x)\)[/tex]. This is incorrect because [tex]\(s(x)\)[/tex] denotes that [tex]\(s\)[/tex] is the function and [tex]\(x\)[/tex] is the variable we input into [tex]\(s\)[/tex].
B. This is the correct interpretation. Here, [tex]\(s(x)\)[/tex] means that the output of the function [tex]\(s\)[/tex] is dependent on the input value [tex]\(x\)[/tex]. In other words, for each value of [tex]\(x\)[/tex], the function [tex]\(s\)[/tex] will provide a corresponding output [tex]\(s(x)\)[/tex].
C. This statement misunderstands the functional notation. It suggests that [tex]\(s\)[/tex] is a value to be multiplied by [tex]\(x\)[/tex], which is not the meaning of [tex]\(s(x)\)[/tex]. [tex]\(s(x)\)[/tex] represents the output of a function [tex]\(s\)[/tex] with input [tex]\(x\)[/tex], not a product.
D. This option claims that there isn't enough information provided to understand what [tex]\(s(x)\)[/tex] represents, but given the common mathematical notation, we do have enough information. [tex]\(s(x)\)[/tex] clearly denotes a function of [tex]\(x\)[/tex].
Therefore, the correct answer is:
B. The value of [tex]\(s(x)\)[/tex] depends on the value of [tex]\(x\)[/tex], since [tex]\(s\)[/tex] is a function of [tex]\(x\)[/tex].
