OCR C3 — Question 5

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
TopicExponential Equations & Modelling

5. The function \(f\) is defined by $$\mathrm { f } ( x ) \equiv 4 - \ln 3 x , \quad x \in \mathbb { R } , \quad x > 0$$
  1. Solve the equation \(\mathrm { f } ( x ) = 0\).
  2. Sketch the curve \(y = \mathrm { f } ( x )\). The function g is defined by $$\mathrm { g } ( x ) \equiv \mathrm { e } ^ { 2 - x } , \quad x \in \mathbb { R }$$
  3. Show that $$\operatorname { fg } ( x ) = x + a - \ln b$$ where \(a\) and \(b\) are integers to be found.