Question

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

Answer 1

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

Answer 2

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

Explanation:

`" "`
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:

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.