IB DP Maths: AA HL复习笔记2.9.3 Modulus Equations & Inequalities

How do I find the modulus of a function?

• How do I solve modulus equations graphically?

• To solve |f(x)| = g(x) graphically
  • Draw y = |f(x)| and y = g(x) into your GDC
  • Find the x-coordinates of the points of intersection

How do I solve modulus equations analytically?

• To solve |f(x)| = g(x) analytically
  • Form two equations
    • f(x) = g(x)
    • f(x) = - g(x)
  • Solve both equations
  • Check solutions work in the original equation

How do I solve modulus inequalities analytically?

• To solve any modulus inequality
  • First solve the corresponding modulus equation
    • Remembering to check whether solutions are valid
  • Then use a graphical method or a sign table to find the intervals that satisfy the inequality
• Another method is to solve two pairs of inequalities
  • For |f(x)| < g(x) solve:
    • f(x) < g(x) when f(x) ≥ 0
    • f(x) > -g(x) when f(x) ≤ 0
  • For |f(x)| > g(x) solve:
    • f(x) > g(x) when f(x) ≥ 0
    • f(x) < -g(x) when f(x) ≤ 0