Period of f(x)=2x-1?

2 Answers

Period is zero or function is non-periodic

Explanation:

The given function

f(x)=2x-1

Let T be the period of f(x) then we have

f(x+T)=f(x)

2(x+T)-1=2x-1

2x+2T=2x-1

2T=0

T=0

The period of given function f(x) is zero hence it is non-periodic

Jul 28, 2018

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color(red)(f(x)=2x-1 is NOT a periodic function.

Explanation:

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A Periodic Function is defined as a function that repeats itself at regular intervals.

These regular intervals are the periods.

A function color(blue)(y=f(x) is periodic with period color(red)(P, if

color(green)(f(x)=f(x+nP) where

color(green)(n takes the values of color(red)(n=1,2,3,4,5 ... and

with color(red)(P being a non-zero constant.

The given function color(green)(y=f(x)=2x-1 represents a linear function as can be seen in the graph below:

enter image source here

As is obvious, the function does not repeat itself at regular intervals.

Hence, color(red)(f(x) != f(x+nP)

Hence color(blue)[[y=f(x)=(2x-1)] is NOT a Periodic Function.

I hope it helps.