\begin{itemize}
\item[6.] If $f(m_1) = \dfrac{m_1 - 1}{m_1 + 1}$, show that
\[
\frac{f(m_1)-f(m_2)}{1 + f(m_1)f(m_2)} = \frac{m_1 - m_2}{1 + m_1m_2}.
\]

\item[7.] If $\phi(x) = a^x$, show that $\phi(y) \cdot \phi(z) = \phi (y + z)$.

\item[8.] Given $\phi(x) = \log \dfrac{1-x}{1+x}$; show that
\[
\phi(x) + \phi(y) = \phi \left(\frac{x+y}{1 + xy}\right).
\]

\item[9.] If $f(\phi) = \cos \phi$, show that
\[
f(\phi) = f(-\phi) = -f(\pi - \phi) = -f(\pi + \phi).
\]

\item[10.] If $F(\theta) = \tan \theta$, show that
\[
F(2\theta) = \frac{2\, F(\theta)}{1 - [F(\theta)]^2}.
\]

\item[11.] Given $\psi(x) = x^{2n} + x^{2m} + 1$; show that
\[
\psi(1) = 3, \quad \psi(0)=1,\quad \psi(a) = \psi(-a).
\]

\item[12.] If $f(x) = \dfrac{2x-3}{x+7}$, find $f(\sqrt{2})$.\hfill \textit{Ans}.~$-.0204$.
\end{itemize}
