Exponential functions are increasing, right?

Algebra Level 4

$\large \color{#302B94}{f(x)=\dfrac{e^x}{e^{\lfloor x \rfloor}}}$

Find the fundamental period of the function $\color{#302B94}{f}$ .

Note : $\lfloor .. \rfloor$ represent the floor function.

1 Doesn't exist,

\because

f is discontinuous function. 0

e

None of the given choices is correct. Doesn't exist,

\because

f is increasing function.

2 solutions

Neha Kannan
May 28, 2015

$x-\lfloor x\rfloor=\{x\}$

So $f(x)=e^{\{x\}}$

Now the function $g(x)=\{x\}$ is periodic with period $1$ . So the period of $f(x)$ is $\boxed{1}$ .

$\mathbb{QED}$

Samuel Job Espartero
Mar 2, 2016

Let the domain of f(x) be the set of integer values. Since the function is periodic, then f(x) is periodic is .