Let f and g be the functions defined by
f : R^2 −→ R^2
(x, y) −→ (−y, −x)
and
g : R^2 −→ R^2
(x, y) −→ (x + 1, y − 1).
(a) Describe the geometric effect of each of f and g
(b) Determine the composite function g◦f.
(c) Show that g is one-to-one and onto, and determine its inverse
function g−1.