OCR C3 2014 June — Question 4

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2014
SessionJune
TopicComposite & Inverse Functions

4 The functions f and g are defined for all real values of \(x\) by $$\mathrm { f } ( x ) = 2 x ^ { 3 } + 4 \quad \text { and } \quad \mathrm { g } ( x ) = \sqrt [ 3 ] { x - 10 }$$
  1. Evaluate \(\mathrm { f } ^ { - 1 } ( - 50 )\).
  2. Show that \(\operatorname { fg } ( x ) = 2 x - 16\).
  3. Differentiate \(\operatorname { gf } ( x )\) with respect to \(x\).