I am looking at the problem set from MIT 18.01 (single variable calculus), in the first problem set I am stuck on this function.
The solution to this function is given as:
The graph is made up of segments joining (0, −6) to (4, 3) to (8, −6). It repeats in a zigzag with period 8. This can be derived using:
(1) ${x\over2} − 1 = −1 =⇒ x = 0$ and $g(0) = 3f(−1) − 3 = −6$
(2) ${x\over2} − 1 = 1 =⇒ x = 4$ and $g(4) = 3f(1) − 3 = 3$
(3) ${x\over2} − 1 = 3 =⇒ x = 8$ and $g(8) = 3f(3) − 3 = −6$
I have understood how the value of x has been derived but can't figure out the respective values at g(0), g(4), g(8).
Could someone tell me how the g(x) or y values have been calculated?