The function f f\,f is defined by
f(x)=(x−3)2+1f(x) = (x - 3)^2 + 1f(x)=(x−3)2+1 for x≥k x \geq k\,x≥k
where k k\,k is a constant.
Given that f−1f^{-1}f−1 exists, state the least possible value of kkk.
In parts (b) to (d), k k\,k takes this least possible value.
Evaluate ff(6)ff(6)ff(6).
Solve the equation f(x)=xf(x) = xf(x)=x.
Explain why your answer to part (c) is also the solution of the equation f(x)=f−1(x)f(x) = f^{-1}(x)f(x)=f−1(x).