A question on Laplace transform

[Debdut]

x(t) and y(t) are related by y(t)=1/(x(t) -k), how should I derive Y(s)/X(s)?

 

[Debdut]

I'm thinking of expanding the inverse term in its Taylor series form. But it would involve terms like (x(t))^2, (x(t))^3, etc if I am right. That would lead to convolution in Laplace domain which according to me is becoming more complicated!

 

[euquila]

I cannot make sense of the question. Here is what I think, y is the "output" and x is the "input" and the relationship is supposed to be y(t) = 1 / x( t - k )
Note I have put the " - k " inside the function argument. This way it has y(t) depending on what x(t) was k seconds ago. This makes more sense since input/output signals in the time domain should be causal and not responding instantaneously. Although maybe I'm missing the point of the question entirely.

 

[euquila]

Then again, why do they put x downstairs without even specifying what it is?