AQA Further Paper 2 2022 June — Question 7

Exam BoardAQA
ModuleFurther Paper 2 (Further Paper 2)
Year2022
SessionJune
TopicComposite & Inverse Functions

7 The function f is defined by $$\mathrm { f } ( x ) = \frac { a x - 5 } { 2 x + b } \quad x \in \mathbb { R } , x \neq \frac { 9 } { 2 }$$ where \(a\) and \(b\) are integers.
The graph of \(y = \mathrm { f } ( x )\) has asymptotes \(x = \frac { 9 } { 2 }\) and \(y = 3\)
7
  1. Find the value of \(a\) and the value of \(b\)
    7
  2. Solve the inequality $$\mathrm { f } ( x ) \leq x + 2$$ Fully justify your answer.