Suppose a space \(Y\) is obtained from a space \(X\) by attaching a single \(n\)-cell
via an attaching map \(f:S^{n-1}\to X\), i.e.
\[ Y=X\cup _f e^n \]
Show that \(H_i(X)\cong H_i(Y)\) for all \(i\) except at most two and give an example where there are two values of \(i\) where the two groups are not isomorphic.