MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Define the rational function f(x)=x+23x−1 for x=−2.
(a) Determine all intervals on the real line where f is (i) continuous and (ii) strictly monotonic.
(b) For each interval identified in part (a), find the corresponding range of f.
(c) For every interval in part (a), justify whether the inverse function f−1 is continuous throughout its domain.
(d) Choose one interval from part (a). Write an explicit formula for f−1 restricted to that interval, and verify the continuity of this inverse at an endpoint of its domain.