The function f is defined by f: x x + 2x 1 for 0

The function f is defined by f: x ↦ x² + 2x − 1 for 0 ≤ x ≤ 2.

a) Express f(x) in the form (x + a)² + b, where a and b are constants.

b) State the range of f.

c) Find an expression for f⁻¹(x), stating its domain.

d)
Show that ff⁻¹ = x.

e)
Sketch on the same diagram the graphs of y = f(x) and y = f⁻¹(x),
making clear the relationship between the graphs.