(a) Show that … is always even

34 (a) Show that $v_{\text{even}}(x)=\frac{1}{2}(v(x)+v(-x))$ is always even. (b) Show that $v_{\text{odd}}(x)=\frac{1}{2}(v(x)-v(-x))$ is always odd.

(a) Show that $v_{\text{even}}(x)=\frac{1}{2}(v(x)+v(-x))$ is always even.
(b) Show that $v_{\text{odd}}(x)=\frac{1}{2}(v(x)-v(-x))$ is always odd.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.6 Properties of the Integral and Average Value, #34