Make x the subject

A question is this type if and only if it asks to rearrange an equation to express x in terms of y or another variable, without explicitly mentioning inverse functions.

3 questions · Moderate -0.6

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Edexcel P3 2022 October Q4
5 marks Moderate -0.8
4. $$y = \log _ { 10 } ( 2 x + 1 )$$
  1. Express \(x\) in terms of \(y\).
  2. Hence, giving your answer in terms of \(x\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) 4.
    1. Express \(x\) in terms of \(y\).
      \(\begin{array} { c } \text { Leave }
      \text { blank } \end{array}\)
      (2)
    2. Hence, giving your answer in terms of \(x\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) \includegraphics[max width=\textwidth, alt={}, center]{83e12fa4-1abb-4bea-bff4-8d36757bd9c3-10_2662_111_107_1950}
OCR MEI C1 2008 June Q5
4 marks Moderate -0.8
5 Make \(x\) the subject of the equation \(y = \frac { x + 3 } { x - 2 }\).
OCR MEI C3 2006 June Q3
7 marks Moderate -0.3
3 Fig. 3 shows the curve defined by the equation \(y = \arcsin ( x - 1 )\), for \(0 \leqslant x \leqslant 2\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{72de4365-c3f0-4106-8daf-3047afeab723-2_684_551_829_758} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure}
  1. Find \(x\) in terms of \(y\), and show that \(\frac { \mathrm { d } x } { \mathrm {~d} y } = \cos y\).
  2. Hence find the exact gradient of the curve at the point where \(x = 1.5\).