(Solved): Computing Fourier series coefficients for a given function is greatly simplified if we consider fi ...

Computing Fourier series coefficients for a given function is greatly simplified if we consider first whether the function is even or odd. Determine whether each of the given functions is even, odd, or neither. (1 point each) a. \( f(x)=\sinh (x)=\left(e^{x}-e^{-x}\right) / 2 \) b. \( f(x)=\sinh \left(x^{2}\right)=\left(e^{x^{2}}-e^{-x^{2}}\right) / 2 \) c. \( f(x)=\sum_{n=0}^{\infty} x^{2 n} / n \) ! (Assume the series converges at all points \( x \).) d. \( f(x)=\sum_{n=0}^{\infty}(x-1)^{2 n} / n \) ! (Assume the series converges at all points \( x \).) e. \( f(x)=x^{2}-1 \) f. \( f(x)=x\left(x^{4}+x^{6}\right) \) g. \( f(x)=\ln (|x+4|) \) h. \( f(x)=x^{2}+4 x+1 \) i. \( f(x)=\sin (\cos (\sin (x))) \) j. \( \quad f(x)=e^{-(x-1)^{2}} \)