Let the Fourier series coefficients of a periodic signal x(t) of fundamental frequency 0 =2/T 0

Let the Fourier series coefficients of a periodic signal x(t) of fundamental frequency Ω₀ =2π/T₀ be {X_k}. Consider the following functions of x(t).

y(t) = 2x(t)−3,    z(t) = x(t − 2) + x(t),         w(t) = x(2t)

Determine if y(t), z(t), and w(t) are periodic, and if so give the corresponding Fourier coefficients in terms of those for x(t).