Further Mathematics Past Questions and Answers

A binary operation * is defined on the set of real numbers, R, by \(x * y = x + y - xy\). If the identity element under the operation * is 0, find the inverse of \(x \in R\).

Solve: \(\sin \theta = \tan \theta\)

Given that \(a^{\frac{5}{6}} \times a^{\frac{-1}{n}} = 1\), solve for n.

Express \(\log \frac{1}{8} + \log \frac{1}{2}\) in terms of \(\log 2\).

If \(f(x) = x^{2}\) and \(g(x) = \sin x\), find g o f.