Practice Symmetric Functions in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Symmetric functions are unchanged under specific variable swaps or sign transformations.
Even functions are symmetric about the y-axis: f(-x) = f(x). Odd functions have 180° rotational symmetry about the origin: f(-x) = -f(x).
Example 1
easyIs the function f(x, y) = x^2 + y^2 + xy symmetric in x and y?
Example 2
mediumExpress x^2 + y^2 in terms of the elementary symmetric polynomials e_1 = x + y and e_2 = xy.
Example 3
mediumIf x + y = 7 and xy = 10, find x^3 + y^3.
Example 4
hardDetermine whether f(x, y, z) = x^2y + y^2z + z^2x is a symmetric function of three variables.