<p>The diagram shows the curve \(y = \mathrm{f}(x)\) which cuts the axes at \(A(0, -a)\) and \(B(b, 0)\), where&nbsp;\(a\) and \(b\) are positive constants.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1779690398443-zoi6ftbg8to.png" style="max-width: min(250px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-paragraph">State, if it is possible to do so, the coordinates of the points where the following curves cut the axes.</div><ol class="i-list"><li><div class="list-item-paragraph">\(y = \mathrm{f}^{-1}(x)\)<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">\(y = \mathrm{f}(x - 2)\)<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">\(y = \mathrm{f}(3x)\)<span class="inline-marks">[1]</span></div></li></ol></li><li><div class="list-item-paragraph">Sketch the curve \(y = \frac{1}{\mathrm{f}(x)}\), stating the equations of any asymptotes and the coordinates of the point where&nbsp;\(y = \frac{1}{\mathrm{f}(x)}\) crosses the axes.<span class="inline-marks">[3]</span></div></li></ol>

The diagram shows the curve \(y = \mathrm{f}(x)\) which cuts the axes at \(A(0, -a)\) and \(B(b, 0)\), where \(a\) and \(b\) are positive constants.

State, if it is possible to do so, the coordinates of the points where the following curves cut the axes.

Sketch the curve \(y = \frac{1}{\mathrm{f}(x)}\), stating the equations of any asymptotes and the coordinates of the point where \(y = \frac{1}{\mathrm{f}(x)}\) crosses the axes.

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