Let and g(x) = cases _ 0 t x f(t), & 0 x 1 x-1, & 1 < x 2 cases Then

MATHEMATICS · Subjective · ISC · Mathematics · Calculus · Calculus

Problem

Let

f(x) = -x^3 + x^2 - x + 1

and

g(x) = \begin{cases} \min_{0 \le t \le x} f(t), & 0 \le x \le 1 \\ x-1, & 1 < x \le 2 \end{cases}

Then, the value of

\lim_{x \to 1} g(g(x))

, is.....