The function f is defined by \(\mathrm{f}(x)=2 x^{2}-6 x+4\) for all real values of \(x\). (a) Write \(\mathrm{f}(x)\) in the form \(a(x+b)^{2}+c\) where \(a, b\) and \(c\) are constants. [3] (b) Hence find the range of f. [1] (c) The function g is defined by \(\mathrm{g}(x)=2 x^{2}-6 x+4\) for \(x \leqslant k\), where \(k\) is a constant. Given that g has an inverse, state the largest possible value of \(k\). [1] (d) The function h is defined by \(\mathrm{h}(x)=\mathrm{e}^{3 x}-1\) for \(x \leqslant 0\). Given that \(\operatorname{gh}(x)\) exists, find \(\operatorname{gh}(x)\), simplifying your answer. [3]

2026 - F/M - 0606/22 | Q1

0/11

0 correct · 0 wrong

The function f is defined by \(\mathrm{f}(x)=2 x^{2}-6 x+...