| Exam Board | SPS |
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| Module | SPS FM Pure (SPS FM Pure) |
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| Year | 2023 |
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| Session | February |
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| Topic | Hyperbolic functions |
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7. (a) Prove that
$$\tanh ^ { - 1 } ( x ) = \frac { 1 } { 2 } \ln \left( \frac { 1 + x } { 1 - x } \right) \quad - k < x < k$$
stating the value of the constant \(k\).
(b) Hence, or otherwise, solve the equation
$$2 x = \tanh ( \ln \sqrt { 2 - 3 x } )$$
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