Which of the following statements is true about functions?

Question

BlackTom AI · Accepted Answer

The question asks which statement is true about functions, and the provided option is: a. A function must specify exactly one value for each argument.

To evaluate this, recall the core definition of a mathematical function: a function from a set A (domain) to a set B (codomain) assigns to every element of A exactly one element of B. When a function has multiple input variables (arguments), its inputs form tuples from the domain, and each such input tuple must map to a single output value. In other words, for every possible argument (in the domain), there is precisely one corresponding output.

This makes option a logically correct in standard mathematical context: there is exactly one output value associated with each input value (each argument).

If we consider potential edge cases, such as partial functions that are not defined for some inputs, then the statement would not hold in that broader sense. However, in the conventional, full-definition sense of a function, every argument from the domain has a unique image, so the statement is true.

Since there are no other answer options provided to compare against, there isn’t additional analysis to contrast for incorrect choices. The emphasis here is on the determinism of a function: a single input cannot correspond to multiple outputs.

Which of the following statements is true about functions?

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