Final answer:
The question seems to ask how to show a function maps real numbers to the interval (-1,1), but without the specific function, a general proof can't be provided. A function like sin(x) can serve as an example that meets this criteria, with all values falling between -1 and 1.
Step-by-step explanation:
The student's question seems incomplete, but it appears to be related to proving whether a given function f is a well-defined function from the real numbers to the set of real numbers between -1 and 1. To show that a function is well-defined, every element in the domain R must have exactly one image in the codomain, and that image must indeed be in the range specified by {x ∈ R : -1 < x < 1}.
Since the question is incomplete, we need to assume a standard function like f(x) = sin(x), which typically maps real numbers to the range (-1,1). We can then show that sin(x) always produces values between -1 and 1 for all x in R, thus satisfying the range condition for the function to be well-defined.
However, without the complete function specified by the student, we cannot provide a step-by-step proof. The student should verify that the function they have satisfies the two conditions for being well-defined when the function's form is known.