Question

Medal will be awarded * Question on Function

Answer 1

Consider the function \[f: A \rightarrow B \] defined by \[f(x) = (x-1)^{2}+4\]
a) Given that\[A= \left\{ x \in \mathbb{R} / x \ge a \right\}\], state te smallest value of a for which f is injective.
b) State the range of f for the domain given in part a)
c) Define the set B so that f is injective
d) Find the inverse function \[f ^{-1}\] of f and state it's domain and range