Further Mathematics 7367: Hyperbolic Functions Topical Past Paper Questions

The function g is defined by $$ \operatorname{g}(x)=\operatorname{sech} x\qquad(x\in\mathbb{R}) $$ Which one of the following is the range of g? Tick (✓) one box. [1 mark] $$ \begin{aligned} &-\infty<g(x)\leq-1\\ &\\ &-1\leq g(x)<0\\ &\\ &0<g(x)\leq1\\ &\\ &1\leq g(x)\leq\infty\\…

It is given that $ f(x) = \cosh^{-1}(x - 3) $ Which of the sets listed below is the greatest possible domain of the function f? Circle your answer. [1 mark] $ \{x : x \geq 4\} $ $ \{x : x \geq 3\} $ $ \{x : x \geq 1\} $ $ \{x : x \geq 0\} $

Which of the following graphs intersects the graph of $ y = \sinh x $ at exactly one point? Circle your answer. [1 mark] $ y = \operatorname{cosech} x $ \quad $ y = \operatorname{cosh} x $ \quad $ y = \operatorname{coth} x $ \quad $ y = \operatorname{sech} x $