Can the domain x repeat in a function?

Answer 1

Oh, what a lovely question! In the world of functions, each input value (x) should correspond to only one output value. This means that the domain (x-values) should not repeat in a function to keep things organized and clear. Just like painting a happy little tree, each branch should have its own place to shine!

Answer 2

The domain x can repeat in a function as long as it represents the same integer throughout the entire function.

* * * * *

The above answer is not true for a number of reasons.

First of all, the domain of a function need not be restricted to integers, as is implied above.

Second, consider f of x, denoted by f(x), which is defined in the following table:

x f(x)

1 2

2 3

1 4

The value x = 1 repeats. In both cases it represents the same integer. However, the corresponding value of f(x) is not the same. The relationship between x and f(x) is one-to-many. Therefore, f(x) is not a function.

Answer 3

Generally speaking, no. But it can be if it is mapped to the same y in the range.