SPS SPS SM Pure 2020 February — Question 9

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2020
SessionFebruary
TopicFunction Transformations
TypeAlgebraic to algebraic transformation description

9
  1. Describe fully a sequence of transformations that map the line \(y = x\) onto the line $$y = 10 - 2 x$$ The function f is defined as \(\mathrm { f } : x \rightarrow 10 - 2 x , x \in R , x \geq 0\).
    The function ff is denoted by g .
  2. Find \(\mathrm { g } ( x )\), giving your answer in a form without brackets.
  3. Determine the domain of g .
  4. Explain whether \(\mathrm { fg } = \mathrm { gf }\).
  5. Find \(\mathrm { g } ^ { - 1 }\) in the form \(\mathrm { g } ^ { - 1 } : x \rightarrow \ldots\)