Let . Three students suggest the following domain restrictions to make invertible: A:…
MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions
Problem
Let q(x)=2x2+8x+5. Three students suggest the following domain restrictions to make q invertible:
A: x≥−2 B: x≤−2 C: −5≤x≤1.
Answer the questions below.
(i) For each proposed restriction, determine whether it actually makes q a bijection. Give a clear justification.
(ii) Obtain the inverse function corresponding to every valid restriction identified in part (i).
(iii) Among the valid restrictions, identify which one produces the largest possible range. Prove that no other interval contained in R yields a larger range for an invertible branch of q.