1.

The curve with equation y = ln (3x) crosses the x-axis at the point P (1/3, 0).

The normal to the curve at the point Q, with x-coordinate q, passes through the origin.

Show that the equation can be rearranged in the form

How can I rearrange this?

2.

a) Sketch the graph of y = e^-x – 1. On the same axes sketch the graph of y = ½ (x - 1), for x ≥ 1, and y = -½ (x - 1), for x < 1. Show the coordinates of the points where the graph meets the axes.

The x-coordinate of the point of intersection of the graphs of α.

b) Show that x = α is a root of the equation x + 2e^-x – 3 = 0.

c) Show that -1<α<0.

I’ve done part a. But how can I do part b & c. Please help me.