Time Invariance of System with x(t) and y(t) Equations

[Drew Carter]

Okay so the question looks like this
Determine whether the system with input x(t) and output y(t) defined by each of the following equations is time
invariant:
(c) y(t) =∫^t+1_t x(τ−α)dt where α is a constant;
(e) y(t) = x(−t);

There are more sub-questions but I was able to solve them. The reason I can't figure this out is the (d) has two items within the x function and the (e) question has a negative t within the x function. Help please. What do I do about the two items and negative t?

 

[Simon Bridge]

What happens when you apply a time delay t -> t+d?

 

[Drew Carter]

What happens when you apply a time delay t -> t+d?

The way I was thought is that for y1(t) your replace x(t) with x1(t), for y2(t) you replace x(t) with x2(t) which then equals x1(t-t0). Then if y2(t)= y1(t-t0). It's time invariant. My issue is doing that with two terms or a negative t

 

[Simon Bridge]

How is that an issue - did you do it and see what happens?
Note: both expressions only have "t" so where do you get "two terms" from?

 

[Drew Carter]

How is that an issue - did you do it and see what happens?
Note: both expressions only have "t" so where do you get "two terms" from?

The first question has T and alpha, that's what I meant by two terms. It's fine, I figured it out