A function \(f\) is defined by \(f(x) = \log_{10}(2 - x)\). Another function \(g\) is defined by \(g(x) = \log_{10}(5 - x)\). The diagram below shows a sketch of the graphs of \(y = f(x)\) and \(y = g(x)\).
\includegraphics{figure_17}
- The point \((c, 1)\) lies on \(y = f(x)\). Find the value of \(c\). [2]
- A point P lies on \(y = f(x)\) and has \(x\)-coordinate \(\alpha\). Another point Q lies on \(y = g(x)\) and also has \(x\)-coordinate \(\alpha\). The distance between P and Q is 1.2 units. Find the value of \(\alpha\), giving your answer correct to three decimal places. [5]