The function f is defined, for \(x \geqslant-1\), by \(\mathrm{f}(x)=1+2^{x}\). (a) Find the range of f. [1] (b) (i) Write down the domain of \(\mathrm{f}^{-1}\). [1] (ii) Find an expression for \(\mathrm{f}^{-1}(x)\). [2] (iii) On the axes, sketch the graph of \(y=\mathrm{f}(x)\) and hence the graph of \(y=\mathrm{f}^{-1}(x)\). State any intercepts with the coordinate axes. [4] ![](https://cdn.mathpix.com/cropped/2eee2c9d-5310-46f8-9644-808d57c4f5b7-08.jpg?height=814&width=914&top_left_y=1825&top_left_x=578) (c) The function g is defined, for \(x \geqslant-1\), by \(\mathrm{g}(x)=x(x+k)\) where \(k\) is a constant. (i) Explain why gf exists. (ii) Find an expression for \(\operatorname{gf}(x)\). (iii) It is given that \(\operatorname{gf}(3)=126\). Find the value of \(k\).

2026 - M/J - 0606/22 | Q8

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The function f is defined, for \(x \geqslant-1\), by \(\m...