Target Mathematics

3.105: Square of a linear function: sketch and inequality

0606/23/M/J/25 — Question 4 · 8 marks

The function ff is defined by f(x)=1−2xf(x) = 1 - 2x for x∈Rx \in \mathbb{R}.
(a)
Explain why the function f2f^{2} can be formed.
[1]
(b)
Sketch y=[f(x)]2=(1−2x)2y = [f(x)]^{2} = (1 - 2x)^{2}, stating intercepts.
[4]
(c)
Given (1−2x)2⩽ax+b(1-2x)^{2} \leqslant ax + b for −1⩽x⩽3-1 \leqslant x \leqslant 3 and no other xx, find aa and bb.
[3]