Q1
Answer
Given $\mathrm{f}(x) = 2x - 5$ for all real values of $x$, and $\mathrm{g}(x) = x^2 - 2x + 5$ for $x < 1$, find:
  1. $\mathrm{fg}(x)$.
  2. $\mathrm{g}^{-1}(x)$.
  1. $2x^2 - 4x + 5$
  2. $1 - \sqrt{x - 4}$
Q2
Answer
Write $\dfrac{4x+7}{(x+1)^2(x+1)}$ in partial fractions.
$\dfrac{1}{x+1} + \dfrac{3}{(x+1)^2} - \dfrac{1}{x+2}$
Q3
Answer
Find the tangent to the curve with equation $$xy^2 + 2x = 3^x$$ at the point $(1,1)$.
$y = mx + c$ where $m = \dfrac{3}{2}(\ln 3 - 1)$ and $c = 1-m$