Determine whether the function is even, odd, or neither. Then describe the symmetry. f(x)=xsqrt (5-x^2) even odd neither Symmetry: x=y symmetry no symmetry x-axis symmetry y-axis symmetry origin symmetry

To determine whether the function \( f(x) = x\sqrt{5 - x^2} \) is even, odd, or neither, we need to check the following properties:1. A function \( f(x) \) is even if \( f(-x) = f(x) \) for all in the domain of .2. A function \( f(x) \) is odd if \( f(-x) = -f(x) \) for all in the domain of .Let's check these properties for \( f(x) \):First, compute \( f(-x) \): Now, compare \( f(-x) \) with \( f(x) \): Clearly, \( f(-x) \neq f(x) \), so the function is not even.Next, check if \( f(-x) = -f(x) \): Since \( f(-x) = -f(x) \), the function is odd.Therefore, the function \( f(x) = x\sqrt{5 - x^2} \) is odd.**Symmetry:**Since the function is odd, it has origin symmetry. that the graph of the function is symmetric with respect to the origin.So, the correct answer is:- odd- Symmetry: origin symmetry