Understanding Unchangedness in Functions

Unchangedness refers to the state of remaining the same or unaltered. In the context of a function, it means that the function does not change its input in any way. The output of the function may be different from the input, but the input itself remains unchanged.

For example, if we have a function `f(x) = x^2`, then the input `x` is passed through the function without any modification, and the output is simply `x^2`. The input `x` remains unchanged, only its value is squared.

In contrast, a function that modifies its input would be one that takes a variable as input, modifies its value, and returns the modified value. For example, a function `g(x) = x + 1` would modify the input `x` by adding 1 to it, so the output would be different from the input.

In summary, unchangedness refers to the idea that the input to a function is not modified or altered in any way, only its value may be transformed or processed to produce an output.