The following WitCH is pretty old, but it came up in a tutorial yesterday, so what the Hell. (It’s also a good warm-up for another WitCH, to appear in the next day or so.) It comes from the 2011 Mathematical Methods Exam 1:
For part (a), the Examination Report indicates that f(g)(x) =√([x+2][x+8]), leading to c = 2 and d = 8, or vice versa. The Report indicates that three quarters of students scored 2/2, “However, many [students] did not state a value for c and d”.
For Part (b), the Report indicates that 84% of students scored 0/2. After indicating the intended answer,
(-∞,-8) U (-2,∞) (-∞,-8] U [-2,∞) or R(-8,-2), the Report goes on to comment:
“This question was very poorly done. Common incorrect responses included [-3,3] (the domain of f(x); x ≥ -2 (as the ‘intersection’ of x ≥ -8 with x ≥ -2); or x ≥ -8 (as the ‘union’ of x ≥ -8 with x ≥ -2). Those who attempted to use the properties of composite functions tended to get confused. Students needed to look for a domain that would make the square root function work.”
The Report does not indicate how students got “confused”, although the composition of functions is briefly discussed in the Study Design (page 72).