CAIE A-Level Mathematics 1.2.4 Graphs of Inverse Functions

CAIE A-Level Mathematics 1.2.4 Graphs of Inverse Functions
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise sketching an inverse by reflecting a one-to-one graph in y = x and transferring intercepts, endpoints, asymptotes and curve shape to exchanged coordinates.

How this is tested

  • draw the mirror line y = x and reflect each key point by exchanging its coordinates
  • transfer intercepts, endpoints and horizontal or vertical asymptotes to their inverse positions
  • preserve the reflected branch and quadrant behaviour without making the curve fold back

Question 10(b)

[Maximum number: 2]

The functions f and g are defined by
f(x)=xfor x⩾0,f(x)=\sqrt{x}\quad\text{for }x\geqslant 0,
and
g(x)=3x+2−5for x⩾−2.g(x)=3\sqrt{x+2}-5\quad\text{for }x\geqslant -2.

Figure for Question 10(b) — CAIE A-Level Mathematics

The diagram shows the graph of y=g(x).

On the diagram sketch the graph of y=g−1(x)y=g^{-1}(x) together with any relevant mirror line.