OCR C3 — Question 1 5 marks

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComposite & Inverse Functions
TypeEvaluate composite at point
DifficultyModerate -0.8 This is a straightforward function composition and inverse function question requiring only basic substitution and solving a simple cubic equation. Both parts are routine C3 exercises with minimal steps: (i) substitute x=1 into g, then into f; (ii) solve x³+4=12 to get x=2. No problem-solving insight needed, just direct application of definitions.
Spec1.02v Inverse and composite functions: graphs and conditions for existence

Functions f and g are defined for all real values of \(x\) by $$f(x) = x^3 + 4 \quad \text{and} \quad g(x) = 2x - 5.$$ Evaluate
  1. fg(1), [2]
  2. \(f^{-1}(12)\). [3]

Functions f and g are defined for all real values of $x$ by
$$f(x) = x^3 + 4 \quad \text{and} \quad g(x) = 2x - 5.$$

Evaluate
\begin{enumerate}[label=(\roman*)]
\item fg(1), [2]
\item $f^{-1}(12)$. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR C3  Q1 [5]}}