The period of the function f (x) 3x + 3 - [3x + 3] + sin (π x/2) , where [ x ] denotes the greatest integer le x, is

Question

The period of the function f (x) 3x + 3 - [3x + 3] + sin (π x/2) , where [ x ] denotes the greatest integer le x, is (A) 4 (B) 1 (C) 2 (D) non-periodic

Tardigrade Admin · Accepted Answer

3x + 3 - [3x + 3] has the period (1/3) and sin (π x/2) has the period (2 π/(π)2) i.e 4 . therefore, the period of f(x) is L.C.M. ( (1/3) , 4) = 4

Q. The period of the function $f (x) 3 x + 3 - [3 x + 3] + sin \frac{π x}{2}$ , where [ x ] denotes the greatest integer $\leq x$ , is

4

1

2

non-periodic

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

Q. The period of the function f(x)3x+3−[3x+3]+sin2πx​ , where [ x ] denotes the greatest integer ≤x, is

4

1

2

non-periodic

3x+3−[3x+3] has the period 31​ and sin2πx​ has the period 2π​2π​ i.e 4 . therefore, the period of f(x) is L.C.M. (31​,4)=4

Q. The period of the function $f (x) 3 x + 3 - [3 x + 3] + sin \frac{π x}{2}$ , where [ x ] denotes the greatest integer $\leq x$ , is

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