when the output is bounded for bounded inputs, then the system is said to be a)stable b) unstable c)functional d) unfunctional please explain

The question refers to the concept of stability in systems, particularly in the context of control theory or signal processing. Let's break down the options provided:

1. Stable: A system is considered stable if, for bounded inputs, the outputs remain bounded as well. This is an essential criterion in many engineering systems to ensure predictable and reliable behavior.

2. Unstable: An unstable system means that bounded inputs can lead to unbounded outputs. Such a system may go into a state where it produces increasingly large outputs in response to small inputs, which is undesirable.

3. Functional: This term generally refers to whether a system can perform its intended functions but does not relate directly to the stability concept.

4. Unfunctional: This is not a standard term in this context. It could imply that the system is non-operational, but it doesn’t convey the specific meaning of stability.

Based on the definitions above, the correct answer is a) stable. This is because a system is defined as stable if its outputs remain bounded when subjected to bounded inputs, which is a fundamental principle in various engineering and mathematical contexts.