OCR C3 — Question 3 7 marks

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComposite & Inverse Functions
TypeFind inverse function
DifficultyModerate -0.8 This is a straightforward C3 inverse functions question requiring basic operations: evaluating a composite function with simple square root arithmetic, finding an inverse by swapping and rearranging (one-step algebra), and sketching reflection in y=x. All parts are routine textbook exercises with no problem-solving or conceptual challenges beyond standard technique recall.
Spec1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence

The function f is defined for all non-negative values of \(x\) by $$f(x) = 3 + \sqrt{x}.$$
  1. Evaluate ff(169). [2]
  2. Find an expression for \(f^{-1}(x)\) in terms of \(x\). [2]
  3. On a single diagram sketch the graphs of \(y = f(x)\) and \(y = f^{-1}(x)\), indicating how the two graphs are related. [3]

The function f is defined for all non-negative values of $x$ by
$$f(x) = 3 + \sqrt{x}.$$

\begin{enumerate}[label=(\roman*)]
\item Evaluate ff(169). [2]
\item Find an expression for $f^{-1}(x)$ in terms of $x$. [2]
\item On a single diagram sketch the graphs of $y = f(x)$ and $y = f^{-1}(x)$, indicating how the two graphs are related. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR C3  Q3 [7]}}