CAIE A-Level Mathematics 1.2.2 Range and Composition

CAIE A-Level Mathematics 1.2.2 Range and Composition
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise finding ranges from formulas and graphs, forming fg or gf in the correct order and deciding whether a composite exists from range and domain restrictions.

How this is tested

  • derive a range from a turning point, endpoint or restricted domain and state its inequality
  • substitute the inner function into the outer function in the stated fg or gf order
  • compare the inner range with the outer domain to find parameter conditions for composition

Question 6

[Maximum number: 5]

Functions f and g are defined by

f(x)=(x+3)2−12 for x⩾0, g(x)=2x−5 for x∈R.\begin{array}{ll} \mathrm{f}(x)=(x+3)^{2}-12 & \text { for } x \geqslant 0, \\ \mathrm{~g}(x)=2 x-5 & \text { for } x \in \mathbb{R} . \end{array}

Question 6(a)

(a)

State the range of f.

[ 1 ]

Question 6(c)

(b)

Solve the equation gf(x)=69.

[ 4 ]