Final answer:
A function from R to R is not possible when the product of f multiplied by another variable equals a constant, resulting in multiple possible outputs for a single input.
Step-by-step explanation:
In order for a function to be defined from R to R, every element of R must have a corresponding output. If the product of f multiplied by another variable equals a constant, it means that for any given input in R, there are multiple possible outputs. This violates the definition of a function, where each input should have a unique output.
In other words, f is not a function from R to R because it fails the horizontal line test. If we were to graph f, we would find that there are horizontal lines that intersect the graph at more than one point, indicating that there are multiple outputs for a single input.
For example, let's say f(x) = k, where k is a constant. If we solve for x, we get x = k/f. Here, k is fixed, but the value of x can vary depending on the value of f. This means that for any given k, we can have multiple possible values for x, which violates the definition of a function.