Let $f: M ightarrow N$ be a homeomorphism. Define a map $f_{star}: pi_{1}left(M, x_{0} ight)

Let $f: M \rightarrow N$ be a homeomorphism. Define a map $f_{\star}: \pi_{1}\left(M, x_{0}\right) \rightarrow$ $\pi_{1}\left(N, f\left(x_{0}\right)\right)$ such that $f_{\star}([\gamma])=[f \circ \gamma]$. Show that $f_{\star}$ is an isomorphism, i.e., that $\pi_{1}\left(M, x_{0}\right) \cong \pi_{1}\left(N, f\left(x_{0}\right)\right)$.