A Quartic Divided by x² − 1

Difficulty: Hard · Topics: Calculus, Derivatives, Continuity

x² − 1 ga bo‘lingan to‘rtinchi darajali funksiya

For a quartic function f(x), let

g(x)=begincasesdfracf(x)x^2-1, & x ≠ 1\\[8pt] -x+a, & x =1endcases

The functions satisfy:

(i) g(x) is differentiable on the set of all real numbers.

(ii) lim x→ 1(f(x))/(g(x)-2)=4.

Find g(a).