This question is related to this one. I'm going through old exams for a 2nd year systems and transforms course, and came across this question. I'm posting this question just in case my other question doesn't actually represent this issue properly...
The question states:
Suppose that we are given the following information about an LTI system: if the input to the system is $x_1[n]=(1/6)^n u[n]$, then the output is $y_1[n]=[a(1/2)^n +10(1/3)^n]u[n]$. If $x_2[n]=(-1)^n$, then the output is $y_2[n]=(7/4)(-1)^n$ where $a$ is a real number. Determine the transfer function of this system and the value of the number $a$.
The solution proceeds by determining the z-transform of $x_1$ and $y_1$ and stating the transfer function as $H(z)=Y_1(z)/X_1(z)$.
However, it seems to me that it's impossible for this system to generate an output of $(1/2)^n+(1/3)^n$ if the input is $(1/6)^n$,and hence the question is somewhat contrived if not outright bogus - see the discussion pertaining to my other question.
What am I missing here?