Given that f(x)=∑n=0∞xnn!f(x) = \sum_{n=0}^{\infty} \frac{x^n}{n!}f(x)=∑n=0∞n!xn, identify the power series representation of the function g(x)=f(x)+f(−x)g(x) = f(x) + f(-x)g(x)=f(x)+f(−x).
∑n=0∞2x2n(2n)!\sum_{n=0}^{\infty} \frac{2x^{2n}}{(2n)!}∑n=0∞(2n)!2x2n
∑n=0∞2x2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{2x^{2n+1}}{(2n+1)!}∑n=0∞(2n+1)!2x2n+1
∑n=0∞x2nn!\sum_{n=0}^{\infty} \frac{x^{2n}}{n!}∑n=0∞n!x2n
∑n=0∞xnn!\sum_{n=0}^{\infty} \frac{x^n}{n!}∑n=0∞n!xn