Final answer:
The organelle associated with β-oxidation in an organism that does not rely on fatty acids as a primary energy source is the peroxisome. Option c is the correct answer.
Step-by-step explanation:
The question is asking which organelle is associated with β-oxidation if a eukaryotic organism does not rely on fatty acids as an energy source. β-oxidation is the process of breaking down fatty acids to generate acetyl-CoA, which then enters the Krebs cycle to produce ATP. β-oxidation begins in the cytoplasm and the mitochondrion is central to this process since the oxidation of fatty acids continues in the mitochondrial matrix.
However, peroxisomes are also heavily involved in the oxidation of very long chain fatty acids and the synthesis of certain lipids. Since the question specifies that the organism does not rely on fatty acids as a primary energy source, it is possible that fewer fatty acids would need to be oxidized in mitochondria.
Thus, peroxisomes may take on the primary role for the β-oxidation process in such organisms, particularly for the breakdown of residual or necessary fatty acids that need to be metabolized for other reasons. Therefore, the correct answer is: C) peroxisome.