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 ${\frac{x}{2}} = 2$
$∴ L CM$ 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 ${\frac{x}{2}} = 2$
$∴ L CM$ of $1, \frac{1}{2}$ and $2$ is $2$