Cho các hàm số :
\(\begin{array}{l}
f\left( x \right) = {x^2} + 2 + \sqrt {2 - x} ;g\left( x \right) = - 2{x^2} - 3x + 5;\\
u\left( x \right) = \left\{ \begin{array}{l}
\sqrt {3 - x} ,\,\,\,\,x < 2\\
\sqrt {{x^2} - 4} ,\,\,x \ge 2
\end{array} \right.;v\left( x \right) = \left\{ \begin{array}{l}
\sqrt {6 - x} ,\,\,\,x \le 0\\
{x^2} + 1,\,\,\,\,\,x > 0
\end{array} \right.
\end{array}\)
Tính các giá trị \(f\left( { - 2} \right) - f\left( 1 \right);g\left( 3 \right);f\left( { - 7} \right) - g\left( { - 7} \right)\)
\(f\left( { - 1} \right) - u\left( { - 1} \right);u\left( 3 \right) - v\left( 3 \right);v\left( 0 \right) - g\left( 0 \right);\frac{{f\left( 2 \right) - f\left( { - 2} \right)}}{{v\left( 2 \right) - v\left( { - 3} \right)}}\)
\(\begin{array}{l}
f\left( { - 2} \right) - f\left( 1 \right) = {\left( { - 2} \right)^2} + 2 + \sqrt {2 + 2} - \left( {{1^2} + 2 + \sqrt {2 - 1} } \right) = 8 - 4 = 4\\
g\left( 3 \right) = - {2.3^3} - 3.3 + 5 = - 58\\
f\left( { - 7} \right) - g\left( { - 7} \right) = {\left( { - 7} \right)^2} + 2 + \sqrt {2 + 7} - \left[ { - 2.{{\left( { - 7} \right)}^3} - 3.\left( { - 7} \right) + 5} \right] = - 658\\
f\left( { - 1} \right) - u\left( { - 1} \right) = {\left( { - 1} \right)^2} + 2 + \sqrt {2 - \left( { - 1} \right)} - \sqrt {3 - \left( { - 1} \right)} = 3 + \sqrt 3 - 2 = 1 + \sqrt 3 \\
u\left( 3 \right) - v\left( 3 \right) = \sqrt {{3^2} - 4} - \left( {{3^2} + 1} \right) = \sqrt 5 - 10\\
v\left( 0 \right) - g\left( 0 \right) = \sqrt {6 - 0} - \left( { - 2.0 - 3.0 + 5} \right) = \sqrt 6 - 5\\
\frac{{f\left( 2 \right) - f\left( { - 2} \right)}}{{v\left( 2 \right) - v\left( { - 3} \right)}} = \frac{{6 - 8}}{{5 - 3}} = \left( { - 1} \right)
\end{array}\)
-- Mod Toán 10