The function f is such that \(\mathrm{f}(x)=3 x^{2}+8 x\) for \(x \geqslant k\), where \(k\) is a constant. It is given that \(\mathrm{f}^{-1}\) exists. \(k\) has the least possible value for which \(\mathrm{f}^{-1}\) exists. (a) Find the value of \(k\). [2] (b) Find the range of f. [2] (c) Find an expression for \(\mathrm{f}^{-1}\). [3] (d) The function g is such that \(\mathrm{g}(x)=3^{x}\) for \(x>-6\). (i) Write down the domain of gf. [1] (ii) Solve the equation \(\operatorname{gf}(x)=27\). [4]

2026 - M/J - 0606/11 | Q6

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The function f is such that \(\mathrm{f}(x)=3 x^{2}+8 x\)...