9709 - 9 marks | Maths4U

A branch, its reflection and one intersection

9 written marks

Let \(f(x)=(x-2)^2+1\), \(x\ge2\).

Find \(f^{-1}\), stating its domain and range.

Sketch both graphs on the same axes with the line \(y=x\). Label the endpoints and one additional reflected pair of points.

Find the exact common point of the two graphs, explaining why another algebraic candidate is rejected.

Complete-answer checking, worked solutions and indicative written criteria.