The inverse of any function is a reflection of the function in the line y=x. Let's draw an arbitrary function, f(x), and the line of reflection, y=x.
To reflect a point in y=x, the segment between the reflected point and original point should be perpendicular to y=x. Since y=x has a slope of 1, any straight line with a slope of - 1 will be perpendicular to it. Using the grid lines, we can draw a line with a slope of - 1 through, for example, the origin. This line will help us sketch a point on the inverse.
Any point on the original function and its corresponding point on the inverse should be equidistant from the line y=x. Using a compass, we can sketch a point on the inverse. Open the compass so that it has a width equal to the distance between y=f(x) and y=x
Keeping the compass setting intact, we can now find the corresponding point on the inverse.
If we repeat this procedure for several more points, we can sketch the inverse.
