Define the notions of function and inverse of a function

1. (a) Define the notions of function and inverse of a function.

(i) f (x) = (x ? 1)2 ? 6, for x? [?1, 7]

(ii) g(x)=cos(3x)+9,forx?R

(b) For each of the functions below find the image set on the given domain:

(iii) h(x) = arcsin(x), for x? [?1, 1]

(c) For each of the three functions f, g and h above,
if the function has an inverse, write the inverse,
if not, write the inverse on one interval where it does exists.

(d) Solve the following equation and inequation, showing your solution in full:

(i) | cos(x)| = ?3 / 2

(ii) sinh(x) ? cosh(x) < 3