A) \[{{Z}_{xx}}={{Z}_{yy}}\]
B) \[{{Z}_{xx}}={{a}^{2}}{{Z}_{yy}}\]
C) \[{{Z}_{yy}}={{a}^{2}}{{Z}_{xx}}\]
D) None of these
Correct Answer: C
Solution :
Given that, \[Z=f(x+ay)+\phi (x-ay)\] \[{{Z}_{x}}=f(x+ay)+\phi (x-ay)\] \[\Rightarrow \] \[{{Z}_{xx}}=f(x+ay)+\phi (x-ay)\] and \[{{Z}_{y}}=af(x+ay)-a\phi (x-ay)\] \[\Rightarrow \] \[{{Z}_{yy}}={{a}^{2}}f(x+ay)-{{a}^{2}}\phi (x-ay)\] Hence,\[{{a}^{2}}{{Z}_{xx}}={{Z}_{yy}}\]
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