Answer:
f(3.14) = 0.86
Step-by-step explanation:
You want the value of f(3.14), given that f(x) = x on the interval [0, 1] and is an even periodic function with a period of 2.
Even function
The fact that f(x) is an even function means f(x) = f(-x).
Period of 2
The fact that f(x) has a period of 2 means that f(x) = f(x -2n) for any integer n.
Value
To evaluate f(3.14), we can reflect the argument into the interval [0, 1].
f(3.14) = f(3.14 -2·2) = f(-0.86) . . . . based on periodicity
f(-0.86) = f(0.86) . . . . . . . . . . . . . . because f(x) is an even function
f(0.86) = 0.86 . . . . . . . . . . . . . . . . from the definition of f(x) on [0, 1]
The value of f(3.14) is 0.86.
