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Problem Let f ( x ) = f 1 ( x ) − 2 f 2 ( x ) f(x) = f_1(x) - 2f_2(x) f ( x ) = f 1 ( x ) − 2 f 2 ( x ) f 1 ( x ) = { min { x 2 , ∣ x ∣ } , ∣ x ∣ ≤ 1 , max { x 2 , ∣ x ∣ } , ∣ x ∣ > 1 , f_1(x) =
\begin{cases}
\min\{x^2, |x|\}, & |x| \le 1,\\
\max\{x^2, |x|\}, & |x| > 1,
\end{cases} f 1 ( x ) = { min { x 2 , ∣ x ∣ } , max { x 2 , ∣ x ∣ } , ∣ x ∣ ≤ 1 , ∣ x ∣ > 1 , f 2 ( x ) = { min { x 2 , ∣ x ∣ } , ∣ x ∣ > 1 , max { x 2 , ∣ x ∣ } , ∣ x ∣ ≤ 1. f_2(x) =
\begin{cases}
\min\{x^2, |x|\}, & |x| > 1,\\
\max\{x^2, |x|\}, & |x| \le 1.
\end{cases} f 2 ( x ) = { min { x 2 , ∣ x ∣ } , max { x 2 , ∣ x ∣ } , ∣ x ∣ > 1 , ∣ x ∣ ≤ 1. g ( x ) = { min { f ( t ) : − 3 ≤ t ≤ x } , − 3 ≤ x < 0 , max { f ( t ) : 0 ≤ t < x } , 0 ≤ x ≤ 3. g(x) =
\begin{cases}
\min\{f(t) : -3 \le t \le x\}, & -3 \le x < 0,\\
\max\{f(t) : 0 \le t < x\}, & 0 \le x \le 3.
\end{cases} g ( x ) = { min { f ( t ) : − 3 ≤ t ≤ x } , max { f ( t ) : 0 ≤ t < x } , − 3 ≤ x < 0 , 0 ≤ x ≤ 3. x ∈ ( − 1 , 0 ) x \in (-1, 0) x ∈ ( − 1 , 0 ) f ( x ) + g ( x ) f(x) + g(x) f ( x ) + g ( x ) x 2 − 2 x + 1 x^2 - 2x + 1 x 2 − 2 x + 1 x 2 + 2 x − 1 x^2 + 2x - 1 x 2 + 2 x − 1 x 2 + 2 x + 1 x^2 + 2x + 1 x 2 + 2 x + 1 x 2 − 2 x − 1 x^2 - 2x - 1 x 2 − 2 x − 1 Browse the problem library