Sketch, on the same axes, the graphs of $y = \ln(4x)$ and $y = \left|x^3 - 2\right|$ for \(

Question

Sketch, on the same axes, the graphs of $y = \ln(4x)$ and $y = \left|x^3 - 2\right|$ for $x > 0$.
Hence, solve the inequality $\left|x^3 - 2\right| > \ln(4x)$.[4]
Using your answer in part (a), find the solution of $\left|\frac{1 - 2x^3}{x^3}\right| + \ln x > \ln 4$ for $x > 0$.[3]
State the solution of the inequality $\left|x^3 - 2\right| < -x$ for $x > 0$.[1]

Accepted Answer

(a) $0 1.57$ (b) $x>1.11$ or $0 0$, there is no solution.

2022 EJC Promo Q4