gaokao 2023 Q23

gaokao · China · national-A-science 10 marks Inequalities Absolute Value Inequality
[Elective 4-5: Inequalities]
Given $f(x) = 2|x - a| - a , \ a > 0$ .
(1) Solve the inequality $f(x) < x$ ;
(2) If the area enclosed by $y = f(x)$ and the coordinate axes is 2 , find $a$ .
[Elective 4-5: Inequalities]

Given $f(x) = 2|x - a| - a , \ a > 0$ .

(1) Solve the inequality $f(x) < x$ ;

(2) If the area enclosed by $y = f(x)$ and the coordinate axes is 2 , find $a$ .