Define by . (i) Show that is not one–to–one on . (ii) Identify two disjoint intervals…
MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Define h:R→R by h(x)=∣2x−6∣+3.
(i) Show that h is not one–to–one on R.
(ii) Identify two disjoint intervals whose union is R such that h becomes one–to–one on each interval.
(iii) For every interval obtained in part (ii), find the corresponding inverse function.
(iv) Sketch the graph of h and the graphs of the inverses obtained, marking key points.