Sketch, on the same axes, the graphs of $y = -2 + 3^x$ and $y = \ln(1 - x^3)$, stating clearly t

Question

Sketch, on the same axes, the graphs of $y = -2 + 3^x$ and $y = \ln(1 - x^3)$, stating clearly the equations of any asymptotes.[4] Hence solve the inequality $\ln(1 - x^3) \le -2 + 3^x$.[2] Using your result in part (ii), solve the inequality $\ln(1 + x^3) \le -2 + \frac{1}{3^x}$.[2]

Accepted Answer

(i) Sketch shown; asymptotes $y=-2$, $x=1$. (ii) $r\le x<1$. (iii) $-1<x\le-r$, where $r=0.5461662555\ldots$ is the intersection abscissa.

2024 MI PRU2 P1 Q8

2024 MI PRU2 P1 Q8

Solution:

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