| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | Specimen |
| Marks | 7 |
| Topic | Composite & Inverse Functions |
| Type | Determine if inverse exists |
| Difficulty | Easy -1.2 This is a straightforward multi-part question testing basic understanding of inverse functions and function composition. Part (i) requires recalling that f(x)=x² fails the horizontal line test (not one-to-one), parts (ii-iii) involve routine algebraic manipulation, and part (iv) 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 |
**Question 3(i)**
- Many-one function or equivalent — B1
**Question 3(ii)**
- Attempt to form $\text{gf}(x)$ — M1
- Obtain $7x^2 - 2$ only — A1
**Question 3(iii)**
- Attempt to make $x$ the subject — M1
- Obtain $\frac{1}{7}(x + 2)$ only — A1
**Question 3(iv)**
- Reflection — B1
- In line $y = x$ — B1
**Total: 7 marks**3 Let $\mathrm { f } ( x ) = x ^ { 2 }$ and $\mathrm { g } ( x ) = 7 x - 2$ for all real values of $x$.\\
(i) Give a reason why f has no inverse function.\\
(ii) Write down an expression for $\operatorname { gf } ( x )$.\\
(iii) Find $\mathrm { g } ^ { - 1 } ( x )$.\\
(iv) Explain the relationship between the graph of $y = \mathrm { g } ( x )$ and $y = \mathrm { g } ^ { - 1 } ( x )$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q3 [7]}}