OCR MEI C3 — Question 6 5 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComposite & Inverse Functions
TypeState domain or range
DifficultyEasy -1.2 This question tests basic recall of even/odd function definitions and straightforward verification by substitution. Part (i) requires stating f(-x) = f(x) and symmetry about the y-axis (pure recall). Part (ii) involves simple algebraic checks with no problem-solving required—all three examples use standard functions where the even/odd property is immediately apparent from basic manipulation.
Spec1.02u Functions: definition and vocabulary (domain, range, mapping)

  1. State the algebraic condition for the function f(x) to be an even function. What geometrical property does the graph of an even function have? [2]
  2. State whether the following functions are odd, even or neither. (A) \(\text{f}(x) = x^2 - 3\) (B) \(\text{g}(x) = \sin x + \cos x\) (C) \(\text{h}(x) = \frac{1}{x + x^3}\) [3]

\begin{enumerate}[label=(\roman*)]
\item State the algebraic condition for the function f(x) to be an even function.

What geometrical property does the graph of an even function have? [2]

\item State whether the following functions are odd, even or neither.

(A) $\text{f}(x) = x^2 - 3$

(B) $\text{g}(x) = \sin x + \cos x$

(C) $\text{h}(x) = \frac{1}{x + x^3}$ [3]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C3  Q6 [5]}}