Domains, ranges and reciprocal hyperbolic functionsAQA A-Level Further Maths: Mind map

Exam questions on Domains, ranges and reciprocal hyperbolic functions

1. Consider the functions $f(x)=\operatorname{sech}x$ and $g(x)=\operatorname{cosech}x$, each defined on its largest possible domain.
   State the range of $g$, and explain why $g$ is not defined at $x=0$.2 marks
2. The function $h$ is defined by $h(x)=\coth x$ on its largest possible domain.
   Find the exact value of $h(\ln3)$.2 marks
3. The function $f$ is defined by $f(x)=\cosh x$ for $x\ge0$.
   State the range of $f$. Explain why $f$ has an inverse function, and state the domain and range of $f^{-1}$.3 marks