First slide

Functions (XII)

Question

Suppose that f is an even, periodic function with period 2, and that $f (x) = x$ for all x in the interval [0, 1]. The value of $[10 f (3 .14)]$ is (where [.] represents the greatest integer function) ______ .

Moderate

Solution

Since f is periodic with period 2 and $f (x) = x \forall x \in [0, 1]$ , and f(x) is even, there is symmetry about y-axis.
Therefore, graph of f(x) is as shown.
$f (3 .14) = 4 - 3 .14 = 0 .86$

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