(Solved): (a) On a single set of axes, sketch the graphs of \( y=1+\operatorname{sech}(x-3) \) and \( y=1+\ ...

(a) On a single set of axes, sketch the graphs of \( y=1+\operatorname{sech}(x-3) \) and \( y=1+\operatorname{sech}^{2}(x-3) \). Reminder: Label each curve and all important features with their values. Give a largest possible interval \( D \) such that the function \( f: D \rightarrow \mathbb{R}, f(x)=1+\operatorname{sech}^{2}(x-3) \) is one-to-one. Hint: If there is more than one possible answer, then choose the most sensible one. (c) Sketch the graph of \( y=f^{-1}(x) \) on your axes from part (a), where \( f^{-1} \) is the inverse function of \( f: D \rightarrow \mathbb{R} \) from part (b). d) Find an expression for \( f^{-1}(x) \) in terms of arccosh. (e) Hence or otherwise, solve \( f(x)=\frac{3}{2} \). Give your answer(s) in terms of log.