Ask AI: Solve the following is either y-axis or origin symmetry or neither,f(x)=X²+3/X²-2

To determine whether a function is symmetric about the y-axis (even), the origin (odd), or neither, we can follow the sytematic way: 1. A function f(x) is symmetric about the y-axis if f(-x) equals f(x). 2. A function f(x) has origin symmetry if f(-x) equals -f(x). Here we have f(x) = (X² + 3) / (X² - 2). Let's perform the symmetry tests: Y-axis symmetry (f(-x) = f(x)): Replace x with -x: f(-x) = ((-x)² + 3) / ((-x)² - 2) = (x² + 3) / (x² - 2) = f(x) Thus, the function f(x) is symmetric about the y-axis. Origin symmetry (f(-x) = -f(x)): We already found that f(-x) = f(x). This is not the same as -f(x), which would be -[(x² + 3) / (x² - 2)]. Thus, the function does not have origin symmetry. In conclusion, the function f(x) = (x² + 3) / (x² - 2) is symmetric about the y-axis but does not have origin symmetry.