Chapter 1, Problem 4PS

Periodic Function The function $f$ is periodic, with period $c.\text{ So},f\left(t+c\right)=f\left(t\right).$ Determine whether each statement is true or false. Explain.

$\left(\text{a}\right)f\left(t-2c\right)=f\left(t\right)\left(\text{b}\right)f\left(t+\frac{1}{2}c\right)=f\left(\frac{1}{2}t\right)$

$\left(\text{c}\right)f\left(\frac{1}{2}\left[t+c\right]\right)=f\left(\frac{1}{2}t\right)\left(\text{d}\right)f\left(\frac{1}{2}\left[t+4c\right]\right)=f\left(\frac{1}{2}t\right)$