OCR MEI C3 2008 June — Question 3 5 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2008
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComposite & Inverse Functions
TypeDetermine if inverse exists
DifficultyModerate -0.8 This question tests basic definitions and recognition of even/odd functions through straightforward substitution. Part (i) requires recall of standard definitions, while part (ii) involves routine checking of f(-x) vs f(x) for three functions with no complex algebraic manipulation needed. This is simpler than average A-level questions which typically require multi-step problem-solving.
Spec1.02u Functions: definition and vocabulary (domain, range, mapping)

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

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

\hfill \mbox{\textit{OCR MEI C3 2008 Q3 [5]}}