One-to-One Function: A function is one-to-one if each element in the domain corresponds to exactly one element in the range. In other words, for each input,...
One-to-One Function:
A function is one-to-one if each element in the domain corresponds to exactly one element in the range. In other words, for each input, there is only one output. No two distinct inputs can have the same output, and each output is associated with only one input.
Example:
The function f(x) = x + 2 is one-to-one, as each input (x) corresponds to exactly one output (x + 2).
The function f(x) = x2 is not one-to-one, as it allows the same output (0) for multiple inputs (0, 1, 2).
Onto Function:
A function is onto if every element in the range corresponds to exactly one element in the domain. In simpler terms, all the output values are "covered" by the range. No output value is left "empty" or "unused".
Example:
The function f(x) = x is onto, as it covers all the possible outputs (0, 1, 2, 3) within the domain (0, 10).
The function f(x) = x2 is not onto, as it only covers a subset of the range (0, 10) for the domain (0, 10).
Into Function:
A function is into if every element in the range corresponds to at least one element in the domain. In simpler terms, all the output values are "reachable" from the domain. No output value is "missing" due to a lack of corresponding input.
Example:
The function f(x) = x + 1 is into, as each input (x) corresponds to exactly one output (x + 1).
The function f(x) = x2 is not into, as it does not ensure that each output value corresponds to exactly one input value