Ask AI: Verify which of the following is either y-axis or origin symmetry or neither, f(x)=X²+3/X²-4x

The given function f(x) = (x² + 3) / (x² - 4x) is neither y-axis symmetric nor origin symmetric. A function is y-axis symmetric if f(x) = f(-x) for all x in the domain. Testing this for the given function, we get: f(-x) = ((-x)² + 3) / ((-x)² - 4(-x)) = (x² + 3) / (x² + 4x), which is not equal to f(x). Hence, the function is not symmetric about the y-axis. A function is origin symmetric if f(-x) = -f(x) for all x in the domain. Testing this for the given function: -f(x) = -((x² + 3) / (x² - 4x)), which is not equal to f(-x). Hence, the function is not symmetric about the origin. Therefore, the function, f(x) = (x² + 3) / (x² - 4x) is neither y-axis symmetric nor origin symmetric.