1. 1
   A function is defined as $f(x) = 2x - 5$ for all real $x$, and $g(x) = x^2$.

   (a)

   What is the value of $f(4)$?

   [1 mark]

   • A$3$
   • B$8$
   • C$13$
   • D$-3$

   (b)

   What is the value of $g(3)$?

   [1 mark]

   • A$6$
   • B$9$
   • C$3$
   • D$1$

   (c)

   What is the value of the composite function $fg(3)$, where $fg(3)$ means $f(g(3))$?

   [1 mark]

   • A$9$
   • B$1$
   • C$13$
   • D$3$

   Total for question 1: 3 marks

2. 2
   The function $h(x) = \frac{1}{x-3}$ is defined for all real $x$ except one value.

   (a)

   State the value of $x$ that must be excluded from the domain of $h$, and explain why.

   [2 marks]

   (b)

   Evaluate $h(5)$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Given $f(x) = 3x + 2$ and $g(x) = x - 4$.

   (a)

   Given $f(x) = 3x + 2$ and $g(x) = x - 4$, find an expression for the composite function $fg(x)$, giving your answer in its simplified form.

   [3 marks]

   (b)

   Find the inverse function $f^{-1}(x)$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A vending machine's cost function is $C(n) = 1.5n + 2$, where $n$ is the number of items bought and $C$ is the total cost in dollars. A loyalty scheme applies the function $L(C) = 0.8C$ to give the discounted cost.

   (a)

   Find an expression for the composite function $LC(n) = L(C(n))$, giving the discounted cost directly in terms of $n$, in simplified form.

   [4 marks]

   (b)

   A customer pays 11.2 dollars after the loyalty discount is applied. Using the composite function $LC(n) = 1.2n + 1.6$, find the number of items, $n$, the customer bought.

   [4 marks]

   (c)

   Find the inverse function $(LC)^{-1}(x)$, and use it to verify your answer to part (b).

   [5 marks]

   Total for question 4: 13 marks

End of questions