<p>The function \(f\) is defined by \(f(x) = 4 - \frac{7}{3x + 2}\), where&nbsp;\(x \in \mathbb{R}, x \neq -\frac{2}{3}\).</p>
<ol class="abc-list"><li data-list-item-id="item-1788163562007-jqe20b2gm" data-list-item-path="item-1788163562007-jqe20b2gm"><div class="list-item-paragraph"><p>Find an expression for \(f^{-1}(x)\).</p><span class="inline-marks">[3]</span></div></li></ol>
<p>The function \(g\) is defined such that&nbsp;\( (f \circ g) \left( \frac{x}{3} \right) = x\).</p>
<ol class="abc-list" start="2"><li data-list-item-id="item-1788163611017-izi071qkm" data-list-item-path="item-1788163611017-izi071qkm"><div class="list-item-paragraph"><p>Using your answer to part (a) or otherwise, find an expression for \(g(x)\).</p><span class="inline-marks">[3]</span></div></li></ol>

The function \(f\) is defined by \(f(x) = 4 - \frac{7}{3x + 2}\), where \(x \in \mathbb{R}, x \neq -\frac{2}{3}\).

<p>Find an expression for \(f^{-1}(x)\).</p>

The function \(g\) is defined such that \( (f \circ g) \left( \frac{x}{3} \right) = x\).

<p>Using your answer to part (a) or otherwise, find an expression for \(g(x)\).</p>

Functions

International Baccalaureate Mathematics: Applications and Interpretation Standard Level