Moderate -0.3 This is a straightforward composite function verification requiring substitution of f(x) into itself, followed by algebraic simplification. The inverse function result follows immediately from the identity ff(x)=x, and the symmetry deduction is a direct consequence. While it requires careful algebra, it's a standard textbook exercise with no novel problem-solving required, making it slightly easier than average.
6 Given that \(\mathrm { f } ( x ) = \frac { x + 1 } { x - 1 }\), show that \(\mathrm { ff } ( x ) = x\).
Hence write down the inverse function \(\mathrm { f } ^ { - 1 } ( x )\). What can you deduce about the symmetry of the curve \(y = \mathrm { f } ( x )\) ?
6 Given that $\mathrm { f } ( x ) = \frac { x + 1 } { x - 1 }$, show that $\mathrm { ff } ( x ) = x$.\\
Hence write down the inverse function $\mathrm { f } ^ { - 1 } ( x )$. What can you deduce about the symmetry of the curve $y = \mathrm { f } ( x )$ ?
\hfill \mbox{\textit{OCR MEI C3 2009 Q6 [5]}}