The period of the function f(x) = e^{x -[x]+| | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$f(x)=e^{\{x\}+|\cos \pi x|+|\cos 2 \pi x|+\cdots+|\cos n \pi x|}$

$f(x)=e^{\{x\}} \cdot e^{|\cos \pi x|} \cdot e^{|\cos 2 \pi x|} \cdot \cdot e^{|

Vedclass · Accepted Answer

$1$

Vedclass · Answer

$f(x)=e^{\{x\}+|\cos \pi x|+|\cos 2 \pi x|+\cdots+|\cos n \pi x|}$

$f(x)=e^{\{x\}} \cdot e^{|\cos \pi x|} \cdot e^{|\cos 2 \pi x|} \cdot \cdot e^{|\cos n \pi x|}$

$f(x)=g(x), h(x)$

Period $f(x)=2(m)$

Reriod $f \quad|\cos x|=\pi$

$y=|\cos x|=|\cos (\pi+x)|=|-\cos x|=|\cos x|=y$

Period of $e^{|\log \pi x|}=\frac{\pi}{\pi}=1$

Period of $e^{\left|(-3)^{2 \pi}\right| x \mid}=\frac{\pi}{2 \pi}=\frac{1}{2}$

Pesiod $f e^{1 \operatorname{los} 3 \pi x}=\frac{\pi}{3 \pi}=\frac{1}{3}$

Period $f e^{|\cos n \pi x|}=\frac{\pi}{n \pi}=\frac{1}{n}$

Perdod of $f(x)=\operatorname{Lcm}\left\{1,1, \frac{1}{2}, \frac{1}{3}, . . \quad \frac{1}{n}\right\}$

$y=\frac{1}{1}=1$

The period of the function $f(x) = e^{x -[x]+|cos\, \pi x|+|cos\, 2\pi x|+....+|cos\, n\pi x|}$ (where $[.]$ denotes greatest integer function); is:-

Similar Questions

Let $f(x) = cos(\sqrt P \,x),$ where $P = [\lambda], ([.]$ is $G.I.F.)$ If the period of $f(x)$ is $\pi$. then

The number of functions $f$, from the set$A=\left\{x \in N: x^{2}-10 x+9 \leq 0\right\}$ to the set $B=\left\{n^{2}: n \in N\right\}$ such that $f(x) \leq(x-3)^{2}+1$, for every $x \in A$, is.

Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then ...... .

The range of the function $f(x) = \frac{{\sqrt {1 - {x^2}} }}{{1 + \left| x \right|}}$ is

Let $S=\{1,2,3,4\}$. Then the number of elements in the set $\{f: S \times S \rightarrow S: f$ is onto and $f(a, b)=f(b, a)$ $\geq a; \forall(a, b) \in S \times S\}$ is