OCR C3 — Question 5

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
TopicComposite & Inverse Functions

5. The function \(f\) is defined by $$f ( x ) \equiv 2 + \ln ( 3 x - 2 ) , \quad x \in \mathbb { R } , \quad x > \frac { 2 } { 3 }$$
  1. Find the exact value of \(\mathrm { ff } ( 1 )\).
  2. Find an equation for the tangent to the curve \(y = \mathrm { f } ( x )\) at the point where \(x = 1\).
  3. Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).