A function of f is periodic with period 3/4. if f(1)=3 and f(17/12)=-2, find f(2/3)?

Question

Hi! I understand how to solve it logically, but is there a way to solve it mathematically?

A function of f is periodic with period 3/4.
if f(1)=3 and f(17/12)=-2,
find f(2/3)

Thanks in advance

Answer 1

Period = 3/4 ===> f(2/3) = f(2/3 + 3/4)
= f( 8/12 + 9/12)
= f(17/12)
= -2

Answer 2

A periodic applications repeats itself. The era is the size of one of its cycles. this implies that if f at some selection x is a, then f at x + the era length is a. f(x) = f(x + T) the place T is the era. think of of it like this, an afternoon is nearly a era. enable's say that at 3oclock the temperature is at that's maximum that's ninety 5 stages. So shall we've some function F(3) = ninety 5. yet 24 hours(one million day) after 3 it somewhat is 3 lower back and the temperature reaches its optimal lower back. so F(3 + 24) = ninety 5, for this reason 24 hours is the era and F(x + 24) = F(x). daily it may repeat this, so it somewhat is a periodic function. So i'm hoping you spot that f(x) = f(x + T) for era T of a periodic function f. Now in case you build on which you would be able to locate that f(x) = f(x + T) = f(x + T + T) = f(x + T + T + T) = f(x + nT) the place n is an Integer. Now to the undertaking, we've f(7) = -2. So all of us understand then that f(7 + 12n) is likewise -2 for any intger n. So if we %. a perfect n, we see that for n = 3 -2 = f(7 + 12n) = f(40 3) for this reason f(40 3) = -2