When can two functions compose?

The functions are $f(x)=\sqrt{x-2}$ for $x\ge2$, and $g(x)=3x^2-6x+5$ for $0\le x\le4$, with real inputs.

(i) Sketch y=f(x) and state its range.2 marks

(ii) Find the inverse of f and its domain.2 marks

(iii) Show that fg exists.2 marks

(iv) Find fg(x) and its range.3 marks

(v) With g now defined on all real numbers, describe fully a sequence of transformations taking y=g(x) to $y=x^2-1$.3 marks

[2023/MI/Promo/PU2/I/8]