The fundamental period of the function f ( x )=| cos π x |+| sin 2 π x |+ ( x /2) is [Note: y denotes the fractional part function of y]

Question

The fundamental period of the function f ( x )=| cos π x |+| sin 2 π x |+ ( x /2) is [Note: y denotes the fractional part function of y] (A) (1/2) (B) 1 (C) 2 (D) 4

Tardigrade Admin · Accepted Answer

Period of | cos π x |=1 Period of | sin 2 π x|=(1/2) and period of (x/2) =2 ∴ LCM of 1, (1/2) and 2 is 2

Q. The fundamental period of the function $f (x) = ∣ cos π x ∣ + ∣ sin 2 π x ∣ + {\frac{x}{2}}$ , is
[Note: ${y}$ denotes the fractional part function of $y]$

$\frac{1}{2}$

1

2

4

Period of $∣ cos π x ∣ = 1$
Period of $∣ sin 2 π x ∣ = \frac{1}{2}$
and period of ${\frac{x}{2}} = 2$
$∴$ LCM of $1, \frac{1}{2}$ and 2 is 2

Q. The fundamental period of the function f(x)=∣cosπx∣+∣sin2πx∣+{2x​}, is [Note: {y} denotes the fractional part function of y]

21​

1

2

4

Period of ∣cosπx∣=1 Period of ∣sin2πx∣=21​ and period of {2x​}=2 ∴ LCM of 1,21​ and 2 is 2

Q. The fundamental period of the function $f (x) = ∣ cos π x ∣ + ∣ sin 2 π x ∣ + {\frac{x}{2}}$ , is
[Note: ${y}$ denotes the fractional part function of $y]$

$\frac{1}{2}$

Period of $∣ cos π x ∣ = 1$
Period of $∣ sin 2 π x ∣ = \frac{1}{2}$
and period of ${\frac{x}{2}} = 2$
$∴$ LCM of $1, \frac{1}{2}$ and 2 is 2