Is $F(x,n)=x(-n + 2)$ time invariant?

1. How do you know if a function is time invariant?
2. Is X (- N time invariant?
3. Is y/n )= x N 2 time invariant?
4. What is the example of time-invariant system?

How do you know if a function is time invariant?

A system is time-invariant if its output signal does not depend on the absolute time. In other words, if for some input signal x(t) the output signal is y1(t)=Trx(t), then a time-shift of the input signal creates a time-shift on the output signal, i.e. y2(t)=Trx(t−t0)=y1(t−t0).

Is X (- N time invariant?

it's not time invariant because it matters where n=0 is.

Is y/n )= x N 2 time invariant?

Hence, the given system is linear. For a system to be time invariant time delay of the input signal leads to an identical time shifts in the input signal. Similarly, when output changes by same amount n₀. Therefore, this system is time invariant.

What is the example of time-invariant system?

b) y(T)=sin[x(T)]

Similarly, if the system is passed through the time delay first then through the system then output will be sinx(T−t). We can see clearly that both the outputs are same. Hence, the system is time invariant.