Step 1: Understanding circulatory systems.
Arthropods, such as insects, crustaceans, and arachnids, have an open circulatory system. This means that their blood (or hemolymph) is not confined to blood vessels but instead bathes the internal organs directly in an open cavity called the hemocoel.
Step 2: Explanation of other options.
- (B) Closed circulatory system: This is found in vertebrates and some invertebrates (e.g., earthworms) where blood flows through a network of vessels.
- (C) No circulatory system: Some small organisms like flatworms and cnidarians lack a circulatory system and rely on diffusion.
- (D) Diffusion through body tissues: While diffusion is essential in small organisms, it is not the primary mode of circulation in arthropods.
Step 3: Conclusion.
The open circulatory system is the hallmark of arthropods for transporting nutrients and gases.
Given, the function \( f(x) = \frac{a^x + a^{-x}}{2} \) (\( a > 2 \)), then \( f(x+y) + f(x-y) \) is equal to