Answer the following questions about one–one functions
MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Answer the following questions about one–one functions.
(a) State the criterion involving horizontal lines that characterises when a real-valued function is one–one.
(b) Prove that this criterion is both necessary and sufficient for injectivity of a function f:R→R.
(c) Using the result of part (b), explain why y=sinx fails to be one–one on R but becomes one–one when its domain is restricted to [−2π,2π]. Determine the corresponding inverse function on this restricted domain.