Question

Is this linear or nonlinear?
\[y(t) = \frac{2x(t)}{2x(t) -1}\]

Answer 1

linear

Answer 2

why?

Answer 3

Because when you simplify it, it is in slope-intercept form

Answer 4

and if the power of the variable is then it is also linear

Answer 5

it's rational though

Answer 6

how does it simplify to slope-intercept form anyway?

Answer 7

did you simplify it correctly so that it is in slope intercept form?

Answer 8

i see nothing that can simplify it further. I can't even turn it into partial fractions

Answer 9

there are a few definitions of linear

Answer 10

a function is linear if:

f(a+b) = f(a) + f(b)

and

f(ka) = k f(a) for some constant k

Answer 11

would it make a difference if I actually said this is a signal function and not just ordinary algebraic function? I don't think it does, but does it?

Answer 12

it might help :) can you define what a signal function is?

Answer 13

i don't know its exact definition but I think it's something that is a function of time

Answer 14

you could use amistre's conditions to test your function:

for example, evaluate it at x=2
then evaluate it at x= 3*2
if it is linear

f( k x) = k f(x)
which means (with k=3)
f(6) = 3 * f(2)

btw, it won't be

Answer 15

i cant find a suitable reference thats readable from the google to help clarify it either

Answer 16

from the looks of setup, it appears to be a rational function what does not conform into a linear or affine nature.


2x-3y = 0 is a linear function

3x+4y-7z = 0 is a linear function

affine functions tend to be constructed as: {linear} + C, for some constant C. And are viewd by many to be "linear"

Answer 17

but even in algebra, i don't think rational functions can be linear right?

Answer 18

generally true