Alan

g(x) = x + 1;

g(y) = y + 1

g(x + y) = x + y + 1

g(x)*g(y) = x*y +x + y + 1

g(x+y) + x*y = x + y + 1 + x*y

wages = hourly rate x hours worked per day x number of days 

I think it means like the following Melody:

Consider n = 9.  The factors of 9 are 1, 3 and 9. That is, there are three factors, so P(9) = 3, which means P(9)^2 = 9.

On the other hand the factors of 6 are 1, 2, 3 and 6 so P(6) = 4, hence P(6)^2 > 6

The question is asking for all the values of n that are like my first example (I think!).

Ok.  Here is one way to do it:

First rearrange both equations in slope-intercept form:

1st eqn:  y = -Vx/(2*(V-1))  + 1/(2*(V-1))   slope =  -V/(2*(V-1))

2nd eqn: y =  -x  + 2/(V - 5)   slope = -1

The two lines will never intersect if they are parallel.  They are parallel if their slopes are the same, so set the two slopes equal to each other and solve for V.  

Try the following reasoning:

A good start would be to graph the function and draw the polygon:

The polygon is clearly a triangle, the area of which is given by (1/2)base*height.  The base length is fairly obvious. To get the height, simply find f(0).

As follows:

Alternatively, you could use Picks theorem for this particular figure.  See https://en.wikipedia.org/wiki/Pick%27s_theorem 

A Ford car left A to B and an Audi car left B to A at the same time. The speed of the Ford car to that of the Audi car was 4:3. The Ford decreased its speed by 25% and the Audi car increased its speed by 25% after they had passed each other. When the Ford car reached B, the Audi car was still 20 km away from A. Find the distance between A and B in km.