| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2019 |
| Session | Specimen |
| Marks | 1 |
| Topic | Composite & Inverse Functions |
| Type | Determine if inverse exists |
| Difficulty | Easy -1.3 This is a straightforward question testing basic understanding of inverse functions and function composition. Part (a) requires recalling that f(x)=x² fails the horizontal line test (not one-to-one), parts (b) and (c) are routine substitution and algebraic manipulation, and part (d) asks for standard knowledge about reflection in y=x. All parts are textbook exercises requiring recall and simple application rather than problem-solving. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02v Inverse and composite functions: graphs and conditions for existence |
(a) Many-one function or equivalent — **B1**
**Total: 1**
(b) Attempt to form $\text{gf}(x)$ — **M1**
Obtain $7x^2 - 2$ only — **A1**
**Total: 2**
(c) Attempt to make $x$ the subject — **M1**
Obtain $\frac{1}{7}(x + 2)$ only — **A1**
**Total: 2**
(d) Reflection — **B1**
In line $y = x$ — **B1**
**Total: 2**3 Let $\mathrm { f } ( x ) = x ^ { 2 }$ and $\mathrm { g } ( x ) = 7 x - 2$ for all real values of $x$.
\begin{enumerate}[label=(\alph*)]
\item Give a reason why f has no inverse function.
\item Write down an expression for $\operatorname { gf } ( x )$.
\item Find $\mathrm { g } ^ { - 1 } ( x )$.
\item Explain the relationship between the graph of $y = \mathrm { g } ( x )$ and $y = \mathrm { g } ^ { - 1 } ( x )$.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2019 Q3 [1]}}