AQA C3 2009 January — Question 5

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
Year2009
SessionJanuary
TopicComposite & Inverse Functions

5 The functions \(f\) and \(g\) are defined with their respective domains by $$\begin{array} { l l } \mathrm { f } ( x ) = 2 - x ^ { 4 } & \text { for all real values of } x
\mathrm {~g} ( x ) = \frac { 1 } { x - 4 } & \text { for real values of } x , x \neq 4 \end{array}$$
  1. State the range of f .
  2. Explain why the function f does not have an inverse.
    1. Write down an expression for fg(x).
    2. Solve the equation \(\operatorname { fg } ( x ) = - 14\).