Find the period of the function

[utkarshakash]

Homework Statement

f(x)=e^3(x-[x])
[] denotes greatest integer function

Homework Equations

The Attempt at a Solution

f(x)=f(x+T)

e^3{x}=e^{x+T}
Taking ln of both sides
3{x}=3{x+T}
{x}={x+T}

x-[x]=x+T-[x+T]
T=[x+T]-[x]

 

[mfb]

Now you have to find T which satisfy this equation.
Alternatively, graph x-[x], the period is obvious in the graph.

 

[utkarshakash]

Now you have to find T which satisfy this equation.
Alternatively, graph x-[x], the period is obvious in the graph.

T=[x]+t-[x]
0=0

How to find T?
Also why you are asking me to draw the graph of x-[x] when the question says e raised to x-[x]?

 

[Saitama]

Also why you are asking me to draw the graph of x-[x] when the question says e raised to x-[x]?

Give it a try at least. ;)

You see that x-[x] which is equivalent to fractional part of x repeats itself after 1. The period of e^(x-[x]) is obvious.