Show that x+a-[x-b],a,b in RR^+, is a periodic function. Find its period.

Aryanna Blake

Aryanna Blake

Answered question

2022-10-14

Show that x + a [ x b ] , a , b R + , is a periodic function. Find its period.

Answer & Explanation

Kenley Rasmussen

Kenley Rasmussen

Beginner2022-10-15Added 13 answers

We know that [ x ] = x { x }, so
x a [ x b ] = x a ( x b { x b } ) = x a x + b + { x b } = b a + { x b } .
Since { x } has period 1, our function also has period 1
shiya43

shiya43

Beginner2022-10-16Added 2 answers

Let f ( x ) = x + a [ x b ] .
Note that [ x + 1 b ] = 1 + [ x b ] .
Therefore, f ( x + 1 ) = ( x + a + 1 ) ( 1 + [ x b ] ) = f ( x ) .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?