| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Session | Specimen |
| Marks | 4 |
| Topic | Composite & Inverse Functions |
| Type | Find inverse function |
| Difficulty | Moderate -0.3 Finding the inverse of a rational function is a standard A-level technique requiring algebraic manipulation (swap x and y, rearrange). The domain restriction follows directly from the original function's range. This is slightly easier than average as it's a straightforward procedural question with no conceptual complications or multi-step problem-solving. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence |
Attempt to make $x$ the subject by collecting $x$ terms on one side M1
Clear attempt seen to interchange the variable with the 3 and 2 interchanged M1
Obtain $y = \frac{3x+1}{x-2}$ aef A1
All real $x$, $x \neq 2$ B1
**Total: 4**2 The function f is defined by $\mathrm { f } ( x ) = \frac { 2 x + 1 } { x - 3 }$ for all real $x , x \neq 3$.
Find an expression for $\mathrm { f } ^ { - 1 } ( x )$ and state the domain of $\mathrm { f } ^ { - 1 }$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 Q2 [4]}}