First slide

Functions (XII)

Question

The period of the function $f (x) = 3 x + 3 - [3 x + 3] + \sin \frac{πx}{2}$ , where [x] denotes the greatest integer ≤ x, is

Moderate

A

4
B

1
C

2
D

Non-periodic

Solution

3x + 3 – [3x + 3] has the period 1 and sin $\frac{πx}{2}$ has the period $\frac{2 π}{π / 2}$ i.e., 4. Therefore, the period of f (x) is L.C.M. (1, 4) = 4.

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