Question

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The piecework rate of a production line is $0.80 for 500 units or fewer, $1.20 for 501 to 750 units, $1.60 for 751 to 1,000 units. If a worker is paid $828, how many pieces of works did he make?

Answer 1

(1) f(x)为奇函数，所以f(0)=0 将x=0代入，解得a=1 (2) f(x)=1-2/(2^x+1) f(x)在R上单调递增。令x1＞x2 f(x1)-f(x2)=1-2/(2^x1+1)-[1-2/(2^x2+1)] =2/(2^x2+1)-2/(2^x1+1)=2(1/(2^x2+1)-1/(2^x1+1)) 2^x在R上递增，x1＞x2 所以，2^x1＞2^x2 2^x1+1＞2^x2+1 1/(2^x1+1)＜1/(2^x2+1) 所以，f(x1)-f(x2)＞0 x1＞x2 所以f(x)在R上单调递增 (3) a=1，f(x)在R上单调递增 f(ax)＜f(x2-2) x＜x2-2 x2-x-2＞0 (x-2)(x+1)＞0 x＜-1或x＞2