a. Consider the function fm,n:[1,∞)→R defined by fm,n(x)=x2+mx+n, where m,n∈R.
b. (i) Starting from fm,n(x1)=fm,n(x2) with x1,x2∈[1,∞), obtain a relation connecting x1−x2 with m and n. Show that either x1=x2 or an additional condition involving m and n must hold.
c. (ii) Deduce all ordered pairs (m,n) for which fm,n is injective on the given domain.