Solving Equations with Modulus Functions (Cambridge (CIE) A Level Maths: Pure 3): Revision Note

Solving equations with modulus functions

How do I sketch modulus equations?

• Two non-parallel straight-line graphs would intersect once

• If a modulus is involved there could be more than one intersection

• Deducing where these intersections are is crucial to solving equations

How do I solve modulus equations?

• STEP 1        Sketch the graphs including any modulus (reflected) parts

  • (see Modulus Functions – Sketching Graphs)

• STEP 2        Locate the graph intersections

• STEP 3       Solve the appropriate equation(s) or inequality

  • For $\left|\mathrm{f}\right(x\left)\right|=\left|\mathrm{g}\right(x\left)\right|$ the two possible equations are $\mathrm{f}\left(x\right)=\mathrm{g}\left(x\right)$ and $\mathrm{f}\left(x\right)=-\mathrm{g}\left(x\right)$