x(t) = 20cos(2π*40t-0.4π)
x(t) = exp(-8πt)
x[n] = exp(cos(2πn/5))
x[n] = u[n] + u[-n]
x[n] = u[n] - u[-n] + 5δ[n]
Many thanks in advance.
$\displaystyle x(t) = 20\cos(80\pi t - 0.4\pi)$x(t) = 20cos(2π*40t-0.4π)
$\displaystyle x(-t) = 20 \cos(-80\pi t - 0.4\pi) = 20\cos[-(80\pi t + 0.4\pi)] = 20 \cos(80\pi t + 0.4\pi)$
final result ... x(-t) is not equal to x(t) or -x(t) ... x(t) is neither even or odd
Sometimes one must just have some prior information.
The function $\displaystyle \cos(x)$ is even and $\displaystyle \sin(x)$ is odd.
On the other hand, you should be able to prove that $\displaystyle f(x)=|x|$ is even.
Can you show that $\displaystyle f(x)=e^x$ is neither even nor odd?